Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 4 (2017), 983-1001.
The degree of the Gauss map of the theta divisor
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.
Algebra Number Theory, Volume 11, Number 4 (2017), 983-1001.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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