Rationality and Brauer group of a moduli space of framed bundles

TL;DR

This paper proves that moduli spaces of framed bundles over smooth projective curves are rational and computes their Brauer group, showing it is zero under certain stability conditions, advancing understanding of their geometric properties.

Contribution

It establishes the rationality of these moduli spaces and determines their Brauer group, providing new insights into their structure and classification.

Findings

Moduli spaces of framed bundles are rational.

Brauer group of these moduli spaces is zero under certain conditions.

Provides explicit computation of the Brauer group.

Abstract

We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.