Kodaira-Saito vanishing and applications

@article{Popa2014KodairaSaitoVA,
  title={Kodaira-Saito vanishing and applications},
  author={Mihnea Cristian Popa},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
  • M. Popa
  • Published 11 July 2014
  • Mathematics
  • arXiv: Algebraic Geometry
The first part of the paper contains a detailed proof of M. Saito's generalization of the Kodaira vanishing theorem, following the original argument and with ample background, based on a lecture given at a Clay workshop on mixed Hodge modules. The second part contains some recent applications, and a Kawamata-Viehweg-type statement in the setting of mixed Hodge modules. 

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We reprove Saito's vanishing theorem for mixed Hodge modules by the method of Esnault and Viehweg. The main idea is to exploit the strictness of direct images on certain branched coverings.

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After explaining the definition of pure and mixed Hodge modules on complex manifolds, we describe some of Saito's most important results and their proofs, and then discuss two simple applications of

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