Singularities of Brill-Noether loci for vector bundles on a curve

TL;DR

This paper investigates the singularities of moduli spaces of stable vector bundles with sections on algebraic curves, extending previous results on generalized theta divisors to a broader context.

Contribution

It generalizes earlier work on the singularities of theta divisors to the setting of Brill-Noether loci for vector bundles on curves.

Findings

Characterization of singularities of Brill-Noether loci

Extension of Laszlo's results to new settings

Insights into the structure of vector bundle moduli spaces

Abstract

In this paper we consider the singularities of the varieties parameterizing stable vector bundles of fixed rank and degree with sections on a smooth curve of genus at least two. In particular, we extend results of Y. Laszlo, and of the second author, regarding the singularities of generalized theta divisors.