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arXiv · 1704.02279

Algebraic fiber spaces and curvature of higher direct images

Bo Berndtsson·Mihai Paun·Xu Wang
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Abstract

In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas, especially in case where the said line bundle satisfies a natural curvature assumption. Several applications are obtained, including a proof of a result by Viehweg-Zuo in the context of a canonically polarized family of maximal variation.

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Bo Berndtsson, Mihai Paun, Xu Wang. 2017-04-07. Algebraic fiber spaces and curvature of higher direct images. https://doi.org/10.1017/s147474802000050x

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