Algebra & Number Theory

The degree of the Gauss map of the theta divisor

Giulio Codogni, Samuel Grushevsky, and Edoardo Sernesi

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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.

Article information

Source
Algebra Number Theory, Volume 11, Number 4 (2017), 983-1001.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842784

Digital Object Identifier
doi:10.2140/ant.2017.11.983

Mathematical Reviews number (MathSciNet)
MR3665643

Zentralblatt MATH identifier
06735377

Subjects
Primary: 14K10: Algebraic moduli, classification [See also 11G15]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14H42: Theta functions; Schottky problem [See also 14K25, 32G20]

Keywords
Gauss map principally polarised abelian varieties Schottky problem V-cycles excess intersection formula

Citation

Codogni, Giulio; Grushevsky, Samuel; Sernesi, Edoardo. The degree of the Gauss map of the theta divisor. Algebra Number Theory 11 (2017), no. 4, 983--1001. doi:10.2140/ant.2017.11.983. https://projecteuclid.org/euclid.ant/1510842784


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