• N RaghaVendra

      Articles written in Proceedings – Mathematical Sciences

    • Determinants of parabolic bundles on Riemann surfaces

      I Biswas N Raghavendra

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      LetX be a compact Riemann surface andMsp(X) the moduli space of stable parabolic vector bundles with fixed rank, degree, rational weights and multiplicities. There is a natural Kähler metric onMsp(X). We obtain a natural metrized holomorphic line bundle onMsp(X) whose Chern form equalsmr times the Kähler form, wherem is the common denominator of the weights andr the rank.

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

      Indranil Biswas N RaghaVendra

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      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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