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Vanishing and injectivity theorems for Hodge modules


Author: Lei Wu
Journal: Trans. Amer. Math. Soc. 369 (2017), 7719-7736
MSC (2010): Primary 14D07; Secondary 14F10, 14F17
DOI: https://doi.org/10.1090/tran/6869
Published electronically: April 7, 2017
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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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Additional Information

Lei Wu
Affiliation: Deparment of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Email: lwu@math.northwestern.edu

DOI: https://doi.org/10.1090/tran/6869
Received by editor(s): October 26, 2015
Received by editor(s) in revised form: November 10, 2015
Published electronically: April 7, 2017
Article copyright: © Copyright 2017 American Mathematical Society