Displaying similar documents to “Hodge-gaussian maps”

Hodge metrics and the curvature of higher direct images

Christophe Mourougane, Shigeharu Takayama (2008)

Annales scientifiques de l'École Normale Supérieure

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Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

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

Indranil Biswas (1997)

Annales de l'institut Fourier

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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.