Brauer group of moduli of parabolic symplectic bundles

TL;DR

This paper computes the Brauer group of the smooth locus of the moduli space of parabolic symplectic stable bundles on a complex projective curve, extending understanding of their geometric and algebraic structure.

Contribution

It provides the first explicit computation of the Brauer group for this class of moduli spaces of parabolic symplectic bundles.

Findings

Brauer group of the moduli space is explicitly determined

Results depend on genus, rank, and parabolic data

Advances understanding of obstructions in moduli problems

Abstract

Let $X$ be a smooth connected complex projective curve of genus $g$, with $g\,\geq\, 3$. Fix an integer $r\geq 2$, a finite subset $D\, \subset\, X$, and a line bundle $L$ on $X$. We compute the Brauer group of the smooth locus of the moduli space of parabolic symplectic stable bundles of rank $r$ on $X$ equipped with a symplectic form taking values in $L(D)$, where $L(D)$ is given the trivial parabolic structure.