• The determinant bundle on the moduli space of stable triples over a curve

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      https://www.ias.ac.in/article/fulltext/pmsc/112/03/0367-0382

    • Keywords

       

      Moduli space; stable triples; determinant bundle; Quillen metric

    • Abstract

       

      We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (E1, E2,ϕ), where E1 and E2 are holomorphic vector bundles over a fixed compact Riemann surfaceX, andϕ: E2 E1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kähler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed C Hermitian vector bundle over a compact Riemann surface.

    • Author Affiliations

       

      Indranil Biswas1 N RaghaVendra1 2

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400 005, India
      2. Advanced Technology Centre, Tata Consultancy Services, K.L.K. Estate, Fateh Maidan Road, Hyderabad - 500 001, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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