Mathematical Research Letters

Volume 13 (2006)

Number 1

Characterizing Jacobians via flexes of the Kummer Variety

Pages: 109 – 123

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n1.a9

Authors

Enrico Arbarello (Università degli Studi di Roma La Sapienza)

Igor Krichever (Columbia University)

Giambattista Marini (Università di Roma Tor Vergata)

Abstract

Given an abelian variety $X$ and a point $a\in X$ we denote by $<a >$ the closure of the subgroup of $X$ generated by $a$. Let $N=2^{g}-1$. We denote by $\kappa: X\to \kappa(X)\subset\mathbb P^N$ 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 $a=2b\in X\setminus\{0\}$ such that $<a >$ is irreducible and $\kappa(b)$ is a flex of $\kappa(X)$.

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