Vanishing and injectivity theorems for Hodge modules

  title={Vanishing and injectivity theorems for Hodge modules},
  author={Lei Wu},
  journal={arXiv: Algebraic Geometry},
  • Lei Wu
  • Published 5 May 2015
  • Mathematics
  • arXiv: Algebraic Geometry
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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