The Hodge theory of algebraic maps

Abstract

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.

66 pages. New results on purity of intersection cohomology and on contractibility criteria added. Original arguments streamlined via weight filtration and two examples discussed in some detail. Presentation improved