• Vector bundles with a fixed determinant on an irreducible nodal curve

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/115/04/0445-0451

• # Keywords

Nodal curves; torsion-free sheaves; fixed determinant

• # Abstract

LetM be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curveX. LetM−L be the closure of its subset consisting of GPBs with fixed determinant− L. We define a moduli functor for whichM−L is the coarse moduli scheme. Using the correspondence between GPBs onX and torsion-free sheaves on a nodal curveY of whichX is a desingularization, we show thatM−L can be regarded as the compactified moduli scheme of vector bundles onY with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves onY. The relation to Seshadri-Nagaraj conjecture is studied.

• # Author Affiliations

1. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400 005, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019