Local structure of Brill-Noether strata in the moduli space of flat stable bundles

TL;DR

This paper investigates the local geometric structure of Brill-Noether strata within the moduli space of flat, stable sheaves on a compact Kähler manifold, revealing they possess quadratic algebraic singularities.

Contribution

It establishes that Brill-Noether strata in this moduli space have quadratic algebraic singularities, providing new insights into their local structure.

Findings

Brill-Noether strata have quadratic algebraic singularities

The study enhances understanding of the local geometry of moduli spaces

Results apply to flat, stable sheaves on compact Kähler manifolds

Abstract

We study the Brill-Noether stratification of the coarse moduli space of locally free stable and flat sheaves of a compact Kahler manifold, proving that these strata have quadratic algebraic singularities.