The Brauer group of desingularization of moduli spaces of vector bundles over a curve

TL;DR

This paper proves that the Brauer group of any desingularization of the moduli space of semistable vector bundles over a smooth projective curve is trivial, providing insights into the geometric structure of these moduli spaces.

Contribution

It establishes the triviality of the Brauer group for desingularizations of moduli spaces of vector bundles over curves, a result not previously known.

Findings

Brauer group of desingularizations is trivial

Results hold for curves of genus at least two

Applicable over algebraically closed fields of characteristic zero

Abstract

Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M_C(r,L) be the coarse moduli space of semistable vector bundles E over C of rank r and determinant L. We show that the Brauer group of any desingularization of M_C(r, L)$ is trivial.