Brauer groups and Picard groups of the moduli of parabolic vector bundles on a nodal curve

Article Type

Research Article

Publication Title

Beitrage Zur Algebra Und Geometrie

Abstract

We determine the Brauer groups and Picard groups of the moduli space UL,pars of stable parabolic vector bundles of rank r with determinant L on a complex nodal curve Y of arithmetic genus g≥2. We also compute the Picard group of the moduli stack for parabolic SL(r)-bundles on Y and use it to give another description of the Picard group of UL,pars. For g≥2, we determine the Brauer group of the moduli space ULs of stable vector bundles on Y of rank r with determinant L, deduce that ULs is simply connected and show the non-existence of the universal bundle on ULs×Y in the non-coprime case.

First Page

751

Last Page

774

DOI

10.1007/s13366-023-00718-7

Publication Date

9-1-2024

Share

COinS