Local structure of theta divisors and related loci of generic curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914719342788608 |
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| author | Budur, Nero |
| author_facet | Budur, Nero |
| contents | For a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit. More generally, any Brill-Noether locus of twisted stable vector bundles on a smooth projective curve is at every point L locally étale isomorphic with its tangent cone if the Petri map at L is injective. This assumption has various consequences for Brill-Noether loci: positive answers to the monodromy conjecture for generalized theta divisors and to questions of Schnell-Yang on log resolutions and Whitney stratifications, and formulas for local b-functions, log canonical thresholds, topological zeta functions, and minimal discrepancies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09250 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local structure of theta divisors and related loci of generic curves Budur, Nero Algebraic Geometry For a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit. More generally, any Brill-Noether locus of twisted stable vector bundles on a smooth projective curve is at every point L locally étale isomorphic with its tangent cone if the Petri map at L is injective. This assumption has various consequences for Brill-Noether loci: positive answers to the monodromy conjecture for generalized theta divisors and to questions of Schnell-Yang on log resolutions and Whitney stratifications, and formulas for local b-functions, log canonical thresholds, topological zeta functions, and minimal discrepancies. |
| title | Local structure of theta divisors and related loci of generic curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2311.09250 |