In this paper we prove a conjecture of Hershel Farkas [11] that if a 4-dimensional principally polarized abelian variety has a vanishing theta-null, and the Hessian of the theta function at the corresponding 2-torsion point is degenerate, the abelian variety is a Jacobian. We also discuss possible generalizations to higher genera, and an interpretation of this condition as an infinitesimal version of Andreotti and Mayer's local characterization of Jacobians by the dimension of the singular locus of the theta divisor.

Jacobians with a vanishing theta-null in genus 4 / Samuel, Grushevsky; SALVATI MANNI, Riccardo. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 164:1(2008), pp. 303-315. [10.1007/s11856-008-0031-4]

Jacobians with a vanishing theta-null in genus 4

SALVATI MANNI, Riccardo
2008

Abstract

In this paper we prove a conjecture of Hershel Farkas [11] that if a 4-dimensional principally polarized abelian variety has a vanishing theta-null, and the Hessian of the theta function at the corresponding 2-torsion point is degenerate, the abelian variety is a Jacobian. We also discuss possible generalizations to higher genera, and an interpretation of this condition as an infinitesimal version of Andreotti and Mayer's local characterization of Jacobians by the dimension of the singular locus of the theta divisor.
2008
01 Pubblicazione su rivista::01a Articolo in rivista
Jacobians with a vanishing theta-null in genus 4 / Samuel, Grushevsky; SALVATI MANNI, Riccardo. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 164:1(2008), pp. 303-315. [10.1007/s11856-008-0031-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/18387
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