The Hodge theory of algebraic maps

Details The Hodge theory of algebraic maps The Hodge theory of algebraic maps

2003-06-02

arxiv.org/abs/math/0306030v2

Mathematics

Algebraic Geometry

66 pages. New results on purity of intersection cohomology and on contractibility criteria added. Original arguments streamlin

Scientific paper

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new Hodge-theoretic results on the cohomology of projective varieties which extend naturally the classical theory and provide new applications.

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