Characterizing Jacobians via flexes of the Kummer variety

2005/02/07 by E. Arbarello, Enrico Arbarello, Giambattista Marini +6
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0502138

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arxiv created 2005/02/08 · arxiv updated 2016/02/16

Abstract

Given an abelian variety X and a point a∈ X we denote by <a> the closure of the subgroup of X generated by a. Let N=2^g-1. We denote by κ: X→ κ(X)⊂\mathbb P^N the map from X to its Kummer variety. We prove that an indecomposable abelian variety X is the Jacobian of a curve if and only if there exists a point a=2b∈ X∖\0\ such that <a> is irreducible and κ(b) is a flex of κ(X).

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