Brauer group and birational type of moduli spaces of torsionfree sheaves on a nodal curve

TL;DR

This paper investigates the Brauer groups and birational properties of moduli spaces of stable and semistable vector bundles on a nodal curve, providing new insights into their algebraic and geometric structure.

Contribution

It computes the Brauer groups of these moduli spaces and explores their rationality, offering novel results on their birational classification.

Findings

Calculated Brauer groups of the moduli spaces.

Analyzed the rationality of the moduli spaces.

Provided conditions for birational equivalence.

Abstract

Let U^{'s}_{L}(n,d) be the moduli space of stable vector bundles of rank $n$ and fixed determinant L of degree d on a nodal curve Y. The moduli space of semistable vector bundles of rank n and degree $d$ will be denoted by U'_Y(n,d). We calculate the Brauer groups of U^{'s}_{L}(n,d)$. We study the question of rationality of $U^{'s}_{L}(n,d)$ and $U'_Y(n,d)$.