The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909080317067264 |
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| author | Podelski, Constantin |
| author_facet | Podelski, Constantin |
| contents | 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 $\mathcal{A}^δ_{t,g-t}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09885 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities Podelski, Constantin Algebraic Geometry 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 $\mathcal{A}^δ_{t,g-t}$ 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. |
| title | The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2309.09885 |