Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space

Biswas, Indranil

Annales de l'Institut Fourier, Tome 47 (1997) no. 3, pp. 885-914.

Nous construisons l’espace de module des fibrés vectoriels stables sur une courbe mobile, et construisons sur cet espace une forme de Weil-Petersson généralisée. En utilisant la formule de Riemann-Roch locale de Bismut-Gillet-Soulé, nous montrons que la forme de Weil-Petersson généralisée est la courbure du fibré déterminant, muni de la métrique de Quillen, pour un fibré vectoriel sur le produit fibré de l’espace de module universel avec la courbe universelle.

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.

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