Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves

Article Type

Research Article

Publication Title

Bulletin des Sciences Mathematiques

Abstract

Let UL′s(n,d) be the moduli space of stable vector bundles of rank n with determinant L where L is a fixed line bundle of degree d over a nodal curve Y. We prove that the projective Poincaré bundle on Y×UL′s(n,d) and the projective Picard bundle on UL′s(n,d) are stable for suitable polarisations. For a nonsingular point x∈Y, we show that the restriction of the projective Poincaré bundle to {x}×UL′s(n,d) is stable for any polarisation. We prove that for arithmetic genus g≥3 and for g=n=2,d odd, the Picard group of the moduli space UL′(n,d) of semistable vector bundles of rank n with determinant L of degree d is isomorphic to Z.

DOI

10.1016/j.bulsci.2020.102930

Publication Date

2-1-2021

Comments

Open Access, Green

This document is currently not available here.

Share

COinS