Characterizing Jacobians via flexes of the Kummer Variety

Enrico Arbarello, Igor Krichever, Giambattista Marini
2006 Mathematical Research Letters  
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) ⊂ 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).
doi:10.4310/mrl.2006.v13.n1.a9 fatcat:2wointktb5eg7alfbymxxtksf4