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
Recommended Citation
Arusha, C.; Bhosle, Usha N.; and Singh, Sanjay Kumar, "Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves" (2021). Journal Articles. 2105.
https://digitalcommons.isical.ac.in/journal-articles/2105
Comments
Open Access, Green