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

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      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

       

      Usha N Bhosle1

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

       
  • Proceedings – Mathematical Sciences | News

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