Mixed Hodge Complexes on Algebraic Varieties

1999/06/13 by Morihiko Saito, Saito, Morihiko · 9 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG #msc:32S35

paper · pdf · doi:10.48550/arxiv.math/9906088

AMSTeX v2.1, 47 pages

arxiv created 1999/06/13 · arxiv updated 2009/11/30

Abstract

We introduce the notion of mixed Hodge complex on an algebraic variety, improving Du Bois' filtered complex, and relate Deligne's theory of mixed Hodge structure with the theory of mixed Hodge module. This was supposed to be true, but is quite nontrivial, because the theory of mixed Hodge module does not work on a simplicial scheme. Some application to the Du Bois singularity is given.

Cited by

• Topology and Euler characteristics of tropical varieties
• Factoriality of normal projective varieties
• Partial Cohomologically Complete Intersections via Hodge Theory
• Multiplier modules, V-filtrations and Bernstein-Sato polynomials on singular ambient varieties
• Inversion of adjunction for higher rational singularities
• Q-factoriality and Hodge-Du Bois theory
• Differential forms on varieties with pre-k-rational singularities
• Local cohomology and singular cohomology of toric varieties via mixed Hodge modules
• Complexes of differential forms and singularities: The injectivity theorem
• A short note on Du Bois singularities

Related

• Mixed Hodge Structures
• Generalization of the theory of mixed Hodge structures and its application
• Mixed Hodge formality
• Characteristic classes of mixed Hodge modules
• An overview of Morihiko Saito's theory of mixed Hodge modules