Local structure of theta divisors and related loci of generic curves
Nero Budur
Journal of Singularities
volume 28 (2025), 181-196
Received: 29 December 2024. In revised form: 2 June 2025.
Abstract:
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.
Author(s) information:
Nero Budur, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
email: nero.budur@kuleuven.be