
TL;DR
This paper provides a detailed proof of Saito's generalization of the Kodaira vanishing theorem and explores recent applications, including a Kawamata-Viehweg-type statement within mixed Hodge modules.
Contribution
It offers a comprehensive proof of Saito's Kodaira vanishing generalization and introduces new applications in the context of mixed Hodge modules.
Findings
Proof of Saito's Kodaira vanishing generalization
New applications in mixed Hodge modules
Kawamata-Viehweg-type statement in this setting
Abstract
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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