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arXiv · 1505.00881

Vanishing and injectivity theorems for Hodge modules

Lei Wu
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Abstract

We prove a surjectivity theorem for the Deligne canonical extension of a polarizable variation of Hodge structure with quasi-unipotent monodromy at infinity along the lines of Esnault-Viehweg. We deduce from it several injectivity theorems and vanishing theorems for pure Hodge modules. We also give an inductive proof of Kawamata-Viehweg vanishing for the lowest graded piece of the Hodge filtration of a pure Hodge module using mixed Hodge modules of nearby cycles.

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Lei Wu. 2015-05-07. Vanishing and injectivity theorems for Hodge modules. https://arxiv.org/abs/1505.00881

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