Hodge-theoretic aspects of the Decomposition Theorem

Details Hodge-theoretic aspects of the Decomposition Theorem Hodge-theoretic aspects of the Decomposition Theorem

2007-10-15

arxiv.org/abs/0710.2708v1

Mathematics

Algebraic Geometry

Suggestions and comments are welcome. Submitted in 02/06 to the editors of the AG Seattle 2005 Proceedings

Scientific paper

Given a projective morphism of compact, complex, algebraic varieties and a relatively ample line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the decomposition isomorphism of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber, yields isomorphisms of pure Hodge structures. The proof is based on a new cohomological characterization of the decomposition isomorphism associated with the line bundle. We prove some corollaries concerning the intersection form in intersection cohomology, the natural map from cohomology to intersection cohomology, projectors and Hodge cycles, and induced morphisms in intersection cohomology.

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