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The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities

Author:
Constantin Podelski
Keyword:
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)
journal:
--
date:
2023-09-17 16:00:00
Abstract
We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal $\mathrm{A}_1$ singularities. This computes the Gauss degree for a general abelian variety in the loci $\mathcal{A}^\delta_{t,g-t}$ 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.
PDF: The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities.pdf
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