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

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).
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
English
KADOMTSEV-PETVIASHVILI EQUATION; CONJECTURE; PROOF
http://arxiv.org/abs/math/0502138
Arbarello, E., Krichever, I., & Marini, G. (2006). Characterizing Jacobians via flexes of the Kummer variety. MATHEMATICAL RESEARCH LETTERS, 13(1), 109-123.
Arbarello, E; Krichever, I; Marini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/38927
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