DETERMINANT BUNDLE OVER THE UNIVERSAL MODULI SPACE OF VECTOR-BUNDLES OVER THE TEICHMULLER SPACE

The moduli space of stable vector bundles over a moving curve is const ructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soule it is show n that the generalized Weil-Petersson form is the curvature of the det erminant line bundle, equipped with the Quillen metric, for a vector b undle on the fiber product of the universal moduli space with the univ ersal curve.