An overview of Morihiko Saito's theory of mixed Hodge modules

Abstract

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 the theory.

45 pages

References in corpus (2)

• Hodge theory of the middle convolution
• On the definition of mixed Hodge modules

Cited by in corpus (17)

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• Gopakumar-Vafa invariants via vanishing cycles
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• Intersection cohomology of rank two character varieties of surface groups
• Vanishing and injectivity theorems for Hodge modules
• Weak positivity for Hodge modules
• Fibration of log-general type space over quasi-abelian varieties
• Weighted multiplier ideals of reduced divisors
• D-modules in birational geometry
• Associated graded of Hodge modules and categorical sl_2 actions
• Hodge ideals of free divisors
• On $V$-filtration, Hodge filtration and Fourier transform
• Hodge-Lyubeznik numbers
• A description of monodromic mixed Hodge modules
• Period integrals and Hodge modules
• On the mixed Hodge structures of the intersection cohomology stalks of complex hypersurfaces
• The deletion restriction method for plane curve germ complement