Given an abelian variety X and a point a is an element of 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 --> K(X) subset of 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 is an element of X \ {0} such that < a > is irreducible and kappa(b) is a flex of kappa(X).
Arbarello, E., Krichever, I., Marini, G. (2006). Characterizing Jacobians via flexes of the Kummer variety. MATHEMATICAL RESEARCH LETTERS, 13(1), 109-123.
Characterizing Jacobians via flexes of the Kummer variety
MARINI, GIAMBATTISTA
2006-01-01
Abstract
Given an abelian variety X and a point a is an element of 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 --> K(X) subset of 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 is an element of X \ {0} such that < a > is irreducible and kappa(b) is a flex of kappa(X).File in questo prodotto:
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