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.

Codogni, G., Grushevsky, S., Sernesi, E. (2017). The degree of the Gauss map of the theta divisor. ALGEBRA & NUMBER THEORY, 11(4), 983-1001 [10.2140/ant.2017.11.983].

The degree of the Gauss map of the theta divisor

CODOGNI, GIULIO;SERNESI, Edoardo
2017-01-01

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.
Codogni, G., Grushevsky, S., Sernesi, E. (2017). The degree of the Gauss map of the theta divisor. ALGEBRA & NUMBER THEORY, 11(4), 983-1001 [10.2140/ant.2017.11.983].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/321237
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