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- W1484180256 abstract "Let $p:sXS$ be a proper Kahler fibration and $sEsX$ a Hermitian holomorphic vector bundle. As motivated by the work of Berndtsson(cite{Berndtsson09a}), by using basic Hodge theory, we derive several general curvature formulas for the direct image $p_*(K_{sX/S}ts sE)$ for general Hermitian holomorphic vector bundle $sE$ in a simple way. A straightforward application is that, if the family $sXS$ is infinitesimally trivial and Hermitian vector bundle $sE$ is Nakano-negative along the base $S$, then the direct image $p_*(K_{sX/S}ts sE)$ is Nakano-negative. We also use these curvature formulas to study the moduli space of projectively flat vector bundles with positive first Chern classes and obtain that, if the Chern curvature of direct image $p_*(K_{X}ts E)$--of a positive projectively flat family $(E,h(t))_{tin mathbb D}X$--vanishes, then the curvature forms of this family are connected by holomorphic automorphisms of the pair $(X,E)$." @default.
- W1484180256 created "2016-06-24" @default.
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- W1484180256 date "2013-03-11" @default.
- W1484180256 modified "2023-09-27" @default.
- W1484180256 title "Curvatures of direct image sheaves of vector bundles and applications I" @default.
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