The Gauss Map on Theta Divisors with Transversal A_1 Singularities
Constantin Podelski
Journal of Singularities
volume 27 (2024), 128-148
Received: 19 February 2024. In revised form: 6 June 2024
Abstract:
We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal A_1 singularities. This computes the Gauss degree for a general abelian variety in the loci A^\delta_{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.