Local structure of theta divisors and related loci of generic curves

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Budur, Nero
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914719342788608
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