The determinant bundle on the moduli space of stable triples over a curve
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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.
KeywordsModuli space stable triples determinant bundle Quillen metric
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