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

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    • 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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      Posted on July 25, 2019

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