The MHM Project

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Description of the project

The
theory of mixed Hodge modules represents a vast
generalization of classical Hodge theory. It was
introduced by Morihiko Saito in two long papers in 1988
and 1990, building on the foundations created by many
people during the 1970s and 1980s, especially in the study
of variations of mixed Hodge structure and their
degenerations, perverse sheaves, and \(\mathscr D\)-module
theory. The theory is very powerful and led to striking
applications right from the beginning, such as

- - a new, complex-analytic proof for the decomposition theorem of Beilinson, Bernstein, Deligne, and Gabber;
- - the construction of pure Hodge structures on the intersection cohomology of projective algebraic varieties;
- - a far-reaching generalization of Kodaira's vanishing theorem.