Vector bundles with a fixed determinant on an irreducible nodal curve

Bhosle, Usha N. (2005) Vector bundles with a fixed determinant on an irreducible nodal curve Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 115 (4). pp. 445-451. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/mathsci/vol115/nov2005/PM2614...

Related URL: http://dx.doi.org/10.1007/BF02829806

Abstract

Let M be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curve X. Let M be the closure of its subset consisting of GPBs with fixed determinant L̅. We define a moduli functor for which M is the coarse moduli scheme. Using the correspondence between GPBs on X and torsion-free sheaves on a nodal curve Y of which X is a desingularization, we show that M can be regarded as the compactified moduli scheme of vector bundles on Y 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 on Y. The relation to Seshadri-Nagaraj conjecture is studied.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Nodal Curves; Torsion-free Sheaves; Fixed Determinant
ID Code:3406
Deposited On:11 Oct 2010 08:50
Last Modified:16 May 2016 14:13

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