Stability and deformations of generalised Picard sheaves

Biswas, I, Brambila-Paz, L and Newstead, PE ORCID: 0000-0002-2498-7992 (2023) Stability and deformations of generalised Picard sheaves. MANUSCRIPTA MATHEMATICA, 173 (1-2). pp. 637-666.

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Official URL: http://dx.doi.org/10.1007/s00229-023-01468-5

Abstract

Let C be a smooth irreducible complex projective curve of genus g≥ 2 and M the moduli space of stable vector bundles on C of rank n and degree d with gcd (n, d) = 1. A generalised Picard sheaf is the direct image on M of the tensor product of a universal bundle on M× C by the pullback of a vector bundle E on C. In this paper, we investigate the stability of generalised Picard sheaves and, in the case where these are locally free, their deformations. When g≥ 3 , n≥ 2 (with some additional restrictions for g= 3 , 4) and the rank and degree of E are coprime, this leads to the construction of a fine moduli space for deformations of Picard bundles.

Item Type:	Article
Uncontrolled Keywords:	14H60, 14J60
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	04 May 2023 09:21
Last Modified:	08 Jan 2024 04:07
DOI:	10.1007/s00229-023-01468-5
Open Access URL:	https://doi.org/10.48550/arXiv.1812.09732
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3170152