The Gauss Map on Theta Divisors with Transversal A₁ Singularities

2023/09/18 by Podelski, Constantin
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.09885

Abstract

We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal A₁ singularities. This computes the Gauss degree for a general abelian variety in the loci A^δ_t,g-t that form some of the irreducible components of the Andreotti-Mayer loci. We also prove that the first coefficient of the Lagrangian specialization is the Samuel multiplicity of the singular locus.

Related

• Gauss map on the theta divisor and Green's functions
• Semicontinuity of Gauss maps and the Schottky problem
• The Gauss map for bielliptic Prym varieties
• The loci of abelian varieties with points of high multiplicity on the theta divisor
• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor