Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space
Indranil Biswas (1997)
Annales de l'institut Fourier
Similarity:
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.