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# Jacobian variety

variety Jis called the Jacobian variety of C. Note that for any ﬁeld k0˙kin which Chas a rational point, deﬁnes an isomorphism Pic 0.C/!J.k/. When Chas a k-rational point, the deﬁnition takes on a more attractive form. A pointed k-scheme is a connected k-scheme together with an element s2S.k/. Abelian varietie Jacobian varieties are the most important class of abelian varieties. Properties Abel-Jacobi map. The Abel-Jacobi map C → J (C) C\to J(C) is defined with help of periods. Line bundles and theta functions. Over the complex numbers, line bundles on a Jacobian variety over a given Riemann surface are naturally encoded by Riemann theta functions. Related concept A Jacobian variety (also: Jacobian) of an algebraic curve S is a principally polarized Abelian variety (cf. also Polarized algebraic variety) (J(S), Θ) formed from this curve. Sometimes a Jacobi variety is simply considered to be a commutative algebraic group Our goal in this chapter is to examine in detail the Jacobian variety which is associated in an intrinsic way with each compact complex manifold of dimension 1. It is the existence of this auxiliary variety that makes the theory of compact manifolds of dimension 1 so much more beautiful and complete than the theory of complex manifolds of higher dimensions. The higher-dimensional theory often still consists of a struggle to resurrect or replace in some special case or other the one. Generally, if C=Kis a curve of genus g, then the Jacobian variety J(C) is an abelian variety having the property that Pic0 C L = J(C)(L) for any eld Lcontaining K. (The precise de nition of J(C) is more subtle. One de nes a certain functor on K-schemes, whose value on Sis a certain group of classes of line bundles on C KS. There are additional subtleties whe

If X is an arbitrary curve over an arbitrary ﬁeld, the Jacobian is an abelian variety that represents the sheaﬁﬁcation of the relative Picard functor. Look in Milne's article or Bosch-Lukt¨ ebohmert-Raynaud Neron Models for more details. Knowing this totally general deﬁnition won't be important for this course, sinc Jacobian variety. The modular abelian varieties that we will encounter later are, by deﬁnition, exactly the quotients of the Jacobian J 1(N) of X 1(N) for some N. In this section we see that merely being a quotient of a Jacobian does not endow an abelian variety with any special properties. Theorem 1.5.4 (Matsusaka). Let Abe an abelian variety over an algebraically closed ﬁeld. Then there. The construction of the Jacobian variety; The canonical maps from the symmetric powers of C to its Jacobian variety; The Jacobian variety as Albanese variety; autoduality; Weil's construction of the Jacobian variety; Generalizations; Obtaining the coverings of curve from its Jacobian; Abelian varieties are quotients of Jacobian varietie Suppose X / Q is a (smooth, projective, geometrically integral) curve of genus g ≥ 2 and J / Q its Jacobian variety. If one is interested in determining the (finite, by Faltings) set of rational points X(Q), then it can be useful to compute J(Q) first The abelian variety J is called the Jacobian variety of C, for any non-singular curve C over the complex numbers. From the point of view of birational geometry , its function field is the fixed field of the symmetric group on g letters acting on the function field of C g

The set of all the normalizedétale mappings on C n of degree d or less can naturally be parametrized on a finite dimensional algebraic space, the so called Jacobian variety, J (n, d), of degree.. deﬁnes a morphism γ: C → Pr.LetJ =Jac(C) be the Jacobian of C. We consider the incidence variety Y ⊂ C ×Pˆr deﬁned by Y = {(p,η) ∈ C ×Pˆr: γ(p) ∈ η}, where Pˆr is the dual projective space ofPr. It has dimension r and possesses the two projections φ˜ and ˜α onto C and Pˆr.Notethat˜α is ﬁnite of degree d and φ˜ is a Pr−1-ﬁbration. We shall writ Let me give an answer for k = C. By a theorem of Matsusaka, every abelian variety A over an algebraic closed field k is a quotient of a Jacobian. Now just apply Matsusaka's theorem to A ∨, and dualize. Since we are over C, dualization sends surjective morphisms of Abelian varieties into injective ones, so we are done

Abstract. This chapter contains a detailed treatment of Jacobian varieties. Sections 2, 5, and 6 prove the basic properties of Jacobian varieties starting from the definition in Section 1, while the construction of the Jacobian is carried out in Sections 3 and 4. The remaining sections are largely independent of one another In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C , hence an abelian variety Algebraic cycles on Jacobian varieties 3. The Fourier transform on a Jacobian 3.1 From now on we take for our abelian variety the Jacobian (J,θ) of a smooth projective curveC of genus g.We choose a base point o ∈ C, which allows us to deﬁne an embeddingϕ: C−→ J by ϕ(p)=OC(p−o).Since we are working modulo algebraic equivalence, all our constructions wil

### Jacobian variety in nLa

• Lernen Sie die Übersetzung für 'jacobian\x20variety' in LEOs Englisch ⇔ Deutsch Wörterbuch. Mit Flexionstabellen der verschiedenen Fälle und Zeiten Aussprache und relevante Diskussionen Kostenloser Vokabeltraine
• The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J with the given point.
• In other words, this theorem relates two diﬀerent approaches to degenerating the Jacobian. Approach 1: the Néron model Viewing the Jacobian J X as the Albanese variety, it is natural to try to extend J U → U by adding degenerate group varieties. This leads to the Néron model. Set-Up:Let A η be an abelian variety over the generic point η of a Dedekind scheme B
• The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus
• ant Jacobian elliptic function Jacobian variety Intermediate field. Abelian varieties appear naturally as Jacobian varieties the.

THE INTERMEDIATE JACOBIAN 285 mann variety of projective lines in P4 and put S = {s E Gr(2, 5): the corresponding line L8 C VI then it is a result of Fano  that S is a smooth irreducible surface having the numerical characters (0.7) hl '(S) = 5, h2'0(S) = 10. Building upon results of Gherardelli  and Todd  we show: (0.8) (Abel's theorem and the Jacobi inversion theorem). In the. In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C, hence an abelian variety. (en) Die Jacobi-Varietät ist ein komplexer -dimensionaler Torus und wird in der Funktionentheorie betrachtet. Der Name geht auf den Mathematiker Carl Gustav Jacob. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J with the given point p. Jacobian determinant. Also called Jacobi determinant. If U, f and y are as above and m = n, the Jacobian determinant of f at y is the determinant of the Jacobian matrix 1. Some authors use the same name for the absolute value of such determinant. If U is an open set and f a locally invertible C 1 map, the absolute value of the Jacobian. Finden Sie perfekte Stock-Fotos zum Thema Jacobian Variety sowie redaktionelle Newsbilder von Getty Images. Wählen Sie aus erstklassigen Inhalten zum Thema Jacobian Variety in höchster Qualität

### Jacobi variety - Encyclopedia of Mathematic

In algebraic geometry a generalized Jacobian is a commutative algebraic group associated to a curve with a divisor, generalizing the Jacobian variety of a complete curve. They were introduced by Maxwell Rosenlicht (), and can be used to study ramified coverings of a curve, with abelian Galois group.Generalized Jacobians of a curve are extensions of the Jacobian of the curve by a commutative. Jacobian Varieties. J.S. Milne. January 4, 2018. Abstract. This is the original TEX file for my article Jacobian Varieties, published as ChapterVII of Arithmetic geometry (Storrs, Conn., 1984), 167212, Springer, New York, 1986.The table of contents has been restored, some corrections and minor improvements tothe exposition have been made, and an index and a some asides added Autor: Luetkebohmert, Werner: dc.contributor.author: Aufnahmedatum: 2019-11-04T13:04:20Z: dc.date.accessioned: In OPARU verfügbar seit: 2019-11-04T13:04:20 By a theorem of Matsusaka, every abelian variety A over an algebraic closed field k is a quotient of a Jacobian. Now just apply Matsusaka's theorem to A ∨, and dualize. Since we are over C, dualization sends surjective morphisms of Abelian varieties into injective ones, so we are done. I think that the slightly weaker version where the field.

edoc-Server Open-Access-Publikationsserver der Humboldt-Universität. de | en. Auflistung nach Schlagwort . edoc-Server Startseit Polarizations and Jacobian varieties. Note that for any . So in some sense the isogeny is more fundamental than the ample line bundle itself. Definition 19 A polarization of an abelian variety is an isogeny such that for some ample line bundle on . is called a principal polarization if is an isomorphism (equivalently, ). Remark 17 Note that a polarization does not necessarily come from a line. многообразие якобиев� The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J with the given point p. Again in this chapter we will assume a certain vague familiarity with the cohomology of sheaves and the theory of line bundles. This material is readily accessible in the modern literature, and some of it can be guessed once one is familiar with Cech cohomology of topological spaces. Our goal in this chapter is to examine in detail the Jacobian variety which is associated in an intrinsic way.

On the Jacobian variety of the Fermat curve | Noriko Yui | download | BookSC. Download books for free. Find book Jacobian variety In mathematics , the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles . It is the connected component of the identity in the Picard group of C , hence an abelian variety Notation and conventions. (0.1) In general, k denotes an arbitrary ﬁeld, k¯ denotes an algebraic closure of k, and k s a separable closure. (0.2) If A is a commutative ring, we sometimes simply write A for Spec(A) On the Jacobian variety of the Fermat curve. The structure of the p -divisible groups arising from Fermat curves over finite fields of characteristic p > 0 is completely determined, up to isogeny, by purely arithmetic means. In certain cases, the global structure of the Jacobian varieties of Fermat curves, up to isogeny, is also determined corresponding family of Jacobian varieties φ: J (C) → X, then R 1 φ ∗ Z ≃ R 1 ω ∗ Z ∗ has a naturally p olarization h· , ·i induced by the intersection form

Jacobian Varieties J.S. Milne August 12, 2012 Abstract This the original TEX file for my article Jacobian Varieties, published as Chapter VII of Arithmetic geometry (Storrs varieties over Q such that, for any A=Q in the family, the Galois representation ˆ A;': G Q! GSp 6 (F ') attached to the '-torsion of Ais surjective. Any such variety Awill be the Jacobian of a genus 3 curve over Q whose respective reductions at two auxiliary primes we prescribe to provide us with generators of Sp 6 (F '). Introductio References In ordinary differential cohomology General. The definition of the Griffith intermediate Jacobian is due to. Phillip Griffiths, Periods of integrals on algebraic manifolds.I Construction and properties of the modular varieties, American Journal of Mathematics 90 (2): 568-626, (1968) doi:10.2307/2373545, ISSN 0002-9327, JSTOR 2373545, MR 022964 Generalized Jacobian variety, line bundles, Picard scheme, stable curve, geometric invariant theory, torus embedding, Neron model, Delony decomposition, Voronoi decomposition, Namikawa decomposition, arrangement of hyperplanes, spng tree, complex-ity of a graph, Kirchhoff-Trent's theorem, elementary cycle, elementary cocycle. 'The main part of this work was done dunng the first authors visit. Introduction []. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version of the Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus.If p is a point of C, then the curve C can be mapped to a subvariety of.

JACOBIAN supports a wide variety of high level concepts, such as inheritance and polymorphism, which help manage the complexity of large models and make a model easier to maintain and evolve. An important feature of the JACOBIAN modeling language is that model development is completely decoupled from model solution. For example, the model of a system may be written once and a variety of. edoc-Server Open-Access-Publikationsserver der Humboldt-Universität. de | en. Auflistung Fakultäten und Institute der HU nach Schlagwor

### The Jacobian Variety SpringerLin

• ABELIAN VARIETIES ISOGENOUS TO A JACOBIAN 591 For any special subset Y $A g;1 over Qa, there exists a CM-point y2A g;1(Qa) such that the isogeny orbit I(y) of yand the special subset Y are disjoint; seeProposition 3.2. We nd it convenient to take yto be a \su ciently general CM point,2 in the sense that the abelian variety A y corresponding to yhas the property that End0(A y) is a CM eld Lof. • JACOBIAN VARIETY AND INTEGRABLE SYSTEM — AFTER MUMFORD, BEAUVILLE AND VANHAECKE REI INOUE, YUKIKO KONISHI, AND TAKAO YAMAZAKI Abstract. Beauville  introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. This can be regarded as a generalization of the Mumford system . In this article. • How the Jacobian helps disease modelling. When I use differential equations to create a mathematical model of a disease (e.g. HIV, Ebola, zombies), I might write something like this: dS dt = Λ−μS−βSI dI dt = βSI -μI −γI. d S d t = Λ − μ S − β S I d I d t = β S I - μ I − γ I. Spread of Ebola in Guinea, Sierra Leone. • Abelian varieties isogenous to a Jacobian Ching-Li Chaiand Frans Oort Final version =14, CLC+FO, October 2011 ABSTRACT. We deﬁne a notion of Weyl CM points in the moduli space A g;1 of g-dimensional principally polarized abelian varieties and show that the Andre-Oort conjecture (or the GRH) implies the following´ statement: for any closed subvariety X$ A g;1 over Qa there exists a Weyl.
• Jacobian varieties with many elliptic curves. Hidalgo, Ruben A. Abstract. In recent years there has been an interest in constructing examples of closed Riemann surfaces whose jacobian varieties are isogenous to a product of many elliptic factors and some other jacobian varieties. The first ones, provided by Ekedahl and Serre, are examples for.
• 1. Introduction. For any positive integer N, let be Shimura's canonical model over of the modular curve of level . Let be the Jacobian variety of over . In this article, we study the rational torsion subgroup of . This kind of investigation began with the work of Ogg (see  and  ), who conjectured that, if is a prime, then where  and.
• Its jacobian variety Jac(C) is a principally polarised abelian variety deﬁned overk. For 1. 2PHILIPPHABEGGER AND FABIEN PAZUKI any abelian varietyAdeﬁned overk we write End( A) for the ring of geometric endomorphisms of A, i.e. the ring of endomorphisms of the base change of A to a given algebraic closure of k. For brevity we say that A has CM if its base change to an algebraic closure of.

### AV -- J.S. Miln

Posts tagged 'Jacobian variety' Jacobi's inversion theorem on May 11, 2014; Abel's Theorem on May 9, 2014; The Abel-Jacobi map on May 5, 2014; Search. Categories. Categories. Tags. Abel-Jacobi map Abel-Jacobi Theorem Abelian varieties Abel summability adjunction Algebraic Number Theory Alternating multilinear map approximation to the identity basis for tensor product Bilinear form. EXPLICIT KUMMER VARIETIES OF HYPERELLIPTIC JACOBIAN THREEFOLDS J.STEFFEN MULLER Abstract. We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is de ned over a eld of characteristic not equal to 2 and has a rational Weierstraˇ point de ned over the same eld. We also construct homogeneous quartic polynomials on the Kummer variety and.

posable Jacobian variety: these are genus 113;161, and 205 (corresponding to N= 672;1152, and 1200, respectively). His techniques are number theoretic and relate to [Ekedahl and Serre 93, Section 2]. In this paper, we use experimental tools to nd many examples of completely decomposable Jacobian varieties in new genera. To nd these examples, we use the action of the automorphism groups on. Title: Jacobian variety and Integrable system -- after Mumford, Beauville and Vanhaecke. Authors: Rei Inoue, Yukiko Konishi, Takao Yamazaki (Submitted on 12 Dec 2005 , last revised 12 Jun 2006 (this version, v2)) Abstract: Beauville introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. May 27, 2020 10:35 Algebraic Surfaces — 11690 9789811215209 page 5 Picard scheme and Jacobian variety 5 topology, we consider a set of ´etale (or ﬂat) morphisms f i: U i → T for i ∈ I such that the union of the images off i covers T.We need som In this paper, a system of coordinates for the elements on the Jacobian Variety of Picard curves is presented. These coordinates possess a nice geometric interpretation and provide us with an unifying environment to obtain an efficient algorithm for the reduction and addition of divisors. Exploiting the geometry of the Picard curves, a completely effective reduction algorithm is developed.

### Motivation for the Jacobian Variety - MathOverflo

Abelian varieties isogenous to a Jacobian Ching-Li Chaiand Frans Oort Version 6.5, CLC+FO, May 5, 2010 x1. Introduction This article was motivated by the following folklore question.1 (1.1) QUESTION.Does there exist an abelian variety A over the ﬁeld Qa of all algebraic numbers which is not isogenous to the Jacobian of a stable algebraic curve over Qa?. ordinary jacobian variety Jo of C and the ordinary canonical map (oo, as de-veloped classically in . The points of a complete nonsingular birational model of C that correspond to the points of CO defining the equivalence relation (these correspond to the valuation rings of k(C)/k which contain o) are called the places of the equivalence relation; by [3, Th. 12] and [3, Th. 8, Cor. 1] the. This is an abelian variety of dimension equal to the genus of the curve and thus carries the helpful structure of a group. To make use of this embedding, we need to know enough about the group of rational points on the Jacobian variety, which can be described by specifying finitely many generators. This group is known as the Mordell-Weil group. The most important fact we need to know is the. Jacobian variety and integrable system - after Mumford, Beauville and Vanhaecke. Rei Inoue, Yukiko Konishi, Takao Yamazaki. SCI - Mathematics; Research output: Contribution to journal › Article › peer-review. 4 Citations (Scopus) Overview; Fingerprint; Abstract. Beauville [A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta. Math. 164. Accordingly, when X is the Jacobian variety of a curve C of genus g, the class [C]\in A^g-1(X) of the image of the Abel-Jacobi mapping is decomposed as [C]=\sum^g-1j=0C(j) with C(j)\in A(j)^g-1(X). \par \it E. Colombo and \it B. van Geemen [Compos. Math. 88, No. 3, 333--353 (1993; Zbl 0802.14002)], proved that for a d-gonal curve the components.

An ambient Jacobian modular abelian variety attached to a congruence subgroup. ModAbVar_ambient_jacobian_class(self, group) Create an ambient Jacobian modular abelian variety. sage: A = J0(37); A Abelian variety J0(37) of dimension 2 sage: type(A) <class 'sage.modular.abvar.abvar_ambient_jacobian.ModAbVar_ambient_jacobian _class'> sage: A.group() Congruence Subgroup Gamma0(37) Functions. Jacobian variety and Integrable system -- after Mumford, Beauville and Vanhaecke Inoue, Rei; Konishi, Yukiko; Yamazaki, Takao; Abstract. Beauville introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. This can be regarded as a generalization of the Mumford system. In this article, we. We will learn how to associate to a given curve an abelian variety known as the Jacobian of the curve. The Torelli theorem states that a curve can be uniquely recovered from its Jacobian. For this purpose we will spend a few meetings discussing basics of abelian varieties. Abiding by the philosophy of our main guiding book [ACGH85] \by curve we shall mean a complete reduced algebraic curve.

### Abelian variety - Wikipedi

The Jacobian variety is the quotient space \mathbb{C}^g/\Lambda, where \Lambda is the \mathbb{Z} linear span of the periods of S. In the talk, we shall see more precisely what this means, and how the Jacobian arises naturally. The Torelli theorem states that given a Jacobian variety, as well as an additional piece of data called the principal polarisation, the compact Rieman surface is. its jacobian variety . In the present paper, first we shall prove that any separable abelian ex-tension of a function field of one variable over a perfect field comes from a pull back of a separable homomorphism onto a suitable generalized jacobian variety of the ground field. Secondly, on the base of the pull back theory, we shall show a theory of class fields of function fields of one. Find the perfect Jacobian Variety stock photos and editorial news pictures from Getty Images. Select from premium Jacobian Variety of the highest quality Vorticesand Jacobian Varieties NicholasS.Manton∗ and NunoM.Roma˜o† ∗ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England † Centre for Quantum Geometry of Moduli Spaces, Institute of Mathematical Sciences, University of Aarhus Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchang

### THE JACOBIAN VARIETY Request PDF - ResearchGat

• Jacobian criterion for projective varieties. Ask Question Asked 7 years, 3 months ago. Active 3 years, 2 months ago. Viewed 2k times 8. 6 $\begingroup$.
• A Jacobian, mathematically, is just a matrix of partial differential equations. You should try and move the robot in a variety of positions and plans and see how it effects the Jacobian. The matrix is rather large, but as you see, it will be different every time! Have fun! For my next post, I'm thinking of some fun computer vision/machine learning projects/tutorials I can post! Stay.
• In this note we prove that a principally polarized abelian variety of dimension g ≤ 3 is the canonically polarized Jacobian variety of a (possibly reducible) algebraic curve; for g = 2 this result was proved by A. Weil. Using results of P. Deligne and D. Mumford on the irreducibility of moduli spaces of stable curves, we thus derive the irreducibility of certain moduli spaces of abelian.
• On a characterization of a Jacobian variety 3 where u o is a fixed point such thatW (u 0) is defined and c is a constant. Let us consider a special case when A =B and Xlet be a positive non-degenerate divisor on A . Let T be the transform of Z x X on A x A by the automorphism (x, y, z)—).(x, y, y—z). When we put W =prT , we have p
• Jacobian variety. Jacobian variety. 雅可比簇K English-Chinese dictionary. 2013. Jacobian; Jacobin; Look at other dictionaries: Jacobian variety — In mathematics, the Jacobian variety of a non singular algebraic curve C of genus g ge; 1 is a particular abelian variety J , of dimension g . The curve C is a subvariety of J , and generates J as a group.Analytically, it can be realized as the.
• Abelian Varieties Spring Quarter, 2015 Deﬁnition 1.2.5. The analytic Jacobian of C is JC = 1(C)=H1(C,Z), a g-dimensional complex torus. Remark 1.2.6. Notice that JC is covariant in C.Namely, a map f: C 0!C induces (C 0) !(C) and f: H1(C 0,Z)!H1(C,Z).One can check that the diagram (C 0)o H1(C 0,Z) (C) o H1(C,Z)is commutative, hence we obtain an induced map on analytic Jacobians
• ered from its principally polarized Jacobian. We also discuss an inﬁnitesimal version of the Torelli theorem. 1. INTRODUCTION The goal is to prove the Torelli theorem for curves: That a curve Ccan be reconstructed from a principally polarized abelian vari-ety. We will start with a brief discussion of Jacobians, then state and prove equivalent versions of the Torelli theorem, and ﬁnally.

### Video: Is every abelian variety a subvariety of a Jacobian

 B. Gross and D. Rohrlich: Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve. Inventiones, Math. 44 (1978) 201-224. | MR 491708 | Zbl 0369.1401 Read JACOBIAN VARIETY OF GENERALIZED FERMAT CURVES, The Quarterly Journal of Mathematics on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips Jacobian varieties 79 5.1. The Picard functor and the deﬁnition of the Jacobian 79 5.2. Basic properties of the Jacobian 80 5.3. The Jacobian as Albanese variety 81 5.4. Jacobians over ﬁnite ﬁelds 82 5.5. Jacobians over C 83 Exercises 84 Chapter 6. 2-descent on hyperelliptic Jacobians 87 6.1. 2-torsion of hyperelliptic Jacobians 87 6.2. Galois cohomology of J 90 6.3. The x−Tmap 91 6. the Jacobian variety J(C) of a hyperelliptic curve C with genus g if 2D 2P 21(mod Pic(C)) for P = (x P;y P) 2C with y P 6= 0. Moreover, if g = 2, we give a more explicit formula for D such that 2D P 1 (mod Pic(C)). 1. Introduction In , Feng and Wu have given a mean value formula for the n-division points on elliptic curves. We recall the de nition of an n-division point of an elliptic curve. Abstract. The isogenous decomposition of the Jacobian variety of classical Fermat curve of prime degree $p \\geq 5$ has been obtained by Aoki using techniques o

### Jacobian Varieties SpringerLin

All the Jacobian varieties appear as orbits of the KP dynamical system. But no other general Abelian varieties appear in this stage, because every finite dimensional orbit should be a (generalized) Jacobian variety. This enables us to give a characterization of the Jacobian varieties among all the Abelian varie- ties. This problem has been long known as the Schottky Problem (, ). I. The Jacobian variety of the Fermat curve has been studied in depth.; Examples of abelian varieties are elliptic curves, Jacobian varieties and K3 surfaces. He was seeking a generalization of the Jacobian variety, by passing from holomorphic line bundles to higher rank.; In 1960 he shared the Cole Prize in algebra with Serge Lang for his work on generalized Jacobian varieties Jacobian varieties. Authors; Authors and affiliations; Lothar Gerritzen; Marius van der Put; Chapter. First Online: 04 October 2006. 485 Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume 817) This is a preview of subscription content, log in to check access. Preview . Unable to display preview. Download preview PDF. Unable to display preview. Download preview PDF. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g , and hence, over the complex numbers, it is a complex torus

### Jacobian variety - Infogalactic: the planetary knowledge cor

Let A be an abelian variety over a p-adic field k and A t its dual. The group of k-rational point A(k) has a p-adic decreasing filtration U A(k). When A = J is a Jacobian variety, we give a precise description of the exact annihilator of U n A(k) with respect to the Tate pairing A(k) × H 1 (k, A t) → ℚ/ℤ.As an application, we give another proof of the result of McCallum in the special. We show that a genus $2$ curve over a number field whose jacobian has complex multiplication will usually have stable bad reduction at some prime. We prove this by computing the Faltings height of the jacobian in two different ways. First, we use a formula by Colmez and Obus specific to the CM case and valid when the CM field is an abelian extension of the rationals. This formula links the. We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a rational Weierstrass point defined over the same field. We also construct homogeneous quartic polynomials on the Kummer variety and show that they represent the duplication map using results of Stoll. Supplementary. This variety is also referred to as the late-flowering type as the first flower opens in midsummer and keeps on flowering through September. The vines become drought-resistant after getting established. 12. Small-Flowered Shrub Clematis. USDA Zone: 3-7. Botanical Name: Clematis 'Stand By Me' clematis showcases a shrub form that doesn't require a trellis. Its stems grow upright with blue.

### jacobian variety - LEO: Übersetzung im Englisch ⇔ Deutsch

1. ant expressions for hyperelliptic functions, (with an Appendix by Shigeki Matsutani: Connection of The formula of Cantor and of Brioschi-Kiepert type)
2. Ambient Jacobian Abelian Variety¶ sage.modular.abvar.abvar_ambient_jacobian.ModAbVar_ambient_jacobian (group) ¶ Return the ambient Jacobian attached to a given congruence subgroup. The result is cached using a weakref. This function is called internally by modular abelian variety constructors. INPUT: group - a congruence subgroup
3. e exact formulas for the maximum and
4. Varieties, also organized by Van Der Geer and Moonen. The spring school was concluded with a workshop, and one of the speakers there was Arnaud Beauville. The title of his lecture was Algebraic cycles on Jacobian varieties and in it he explained what his paper  was about. The construction of the Chow ring an
5. The Jacobian variety of an algebraic curve (1954) by W-L Chow Venue: Amer. J. Math: Add To MetaCart. Tools. Sorted by: Results 1 - 6 of 6. Abelian varieties by J. S. Milne , 2008 These notes are an introduction to the theory of abelian varieties, including the arithmetic of abelian varieties and Faltings's proof of certain finiteness theorems. The orginal version of the notes was.

### Jacobian variety - WikiMili, The Best Wikipedia Reade

351 Abelian surfaces and Jacobian varieties over finite fields HANS-GEORG RÜCK Fachbereich 9 Mathematik, Universität des Saarlands, D-6600 Saarbrücken, Federal Republic of Germany Compositio Mathematica Mathematic International Conference on Jacobian varieties, Abelian functions, and Kummer surfaces (held at the room K-21, University of Yamanashi; 2012, 30-31, March. Organized by Yoshihiro Ônishi) Speakers and Abstracts. England, Matthew (Glasgow Univ.) : Building Abelian functions with generalised Hirota operators Abstract: We consider symmetric generalisations of Hirota's bilinear operator and in.

### Jacobian variety - HandWik

• Journal Finder . Root numbers for the Jacobian varieties of Fermat curves. DOI: 10.1016/j.jnt.2021.03.01
• The Jacobian modules of a representation of a Lie algebra and geometry of commuting varieties Dmitrii I. Panyushev February 12, 1993 (0.1) Let 9 be a finite-dimensionalLie algebra over an algebraieally closed field k of eharaeteristik O. Cqnsider a finite-dimensionalrepresentation p : 9 ~gl(V). By V· we denote the dual g-module. Two bilinear mapping
• Verfasst von: Viljamaa, Matti : Titel: On the structure of generalized Jacobian varieties: Verf.angabe: Matti Viljamaa: Verlagsort: Helsinki: Verlag: Suomalainen.
• For some algorithms the jacobian must be supplied as well, the form of this should be a function return a list of lists of the form [[df_1/dy_1, There are a variety of algorithms available for different types of systems. Possible algorithms are. rkf45 - runga-kutta-felhberg (4,5) rk2 - embedded runga-kutta (2,3) rk4 - 4th order classical runga-kutta. rk8pd - runga-kutta prince-dormand (8,9.
• Jacobian variety - algebraic curves

### About: Jacobian variety - dbpedia

1. Jacobian_variety : definition of Jacobian_variety and
2. Jacobian - Encyclopedia of Mathematic
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4. Jacobian variety — Wikipedia Republished // WIKI  ### Generalized Jacobian - Wikipedi

1. Jacobian Varieties - James Milne -- Home basic properties
2. Jacobian Varietie
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4. Abelian Varieties - lcc
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