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2017 The degree of the Gauss map of the theta divisor
Giulio Codogni, Samuel Grushevsky, Edoardo Sernesi
Algebra Number Theory 11(4): 983-1001 (2017). DOI: 10.2140/ant.2017.11.983

Abstract

We study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. Thanks to this analysis, we obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus. We spell out this bound in several examples, and we use it to understand the local structure of isolated singular points. We further define a stratification of the moduli space of ppavs by the degree of the Gauss map. In dimension four, we show that this stratification gives a weak solution of the Schottky problem, and we conjecture that this is true in any dimension.

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Giulio Codogni. Samuel Grushevsky. Edoardo Sernesi. "The degree of the Gauss map of the theta divisor." Algebra Number Theory 11 (4) 983 - 1001, 2017. https://doi.org/10.2140/ant.2017.11.983

Information

Received: 17 August 2016; Revised: 10 January 2017; Accepted: 11 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06735377
MathSciNet: MR3665643
Digital Object Identifier: 10.2140/ant.2017.11.983

Subjects:
Primary: 14K10
Secondary: 14C17, 14H42

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2017
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