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

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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.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India

    Indranil Biswas & N. RaghaVendra

  2. Advanced Technology Centre, Tata Consultancy Services, K.L.K. Estate, Fateh Maidan Road, 500 001, Hyderabad, India

    N. RaghaVendra

Authors
  1. Indranil Biswas
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  2. N. RaghaVendra
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Correspondence to Indranil Biswas.

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Biswas, I., RaghaVendra, N. The determinant bundle on the moduli space of stable triples over a curve. Proc. Indian Acad. Sci. (Math. Sci.) 112, 367–382 (2002). https://doi.org/10.1007/BF02829790

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  • DOI: https://doi.org/10.1007/BF02829790

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