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Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space. (English) Zbl 0873.32017
Summary: The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.

32G13 Complex-analytic moduli problems
14D20 Algebraic moduli problems, moduli of vector bundles
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