The Hodge theory of algebraic maps
Algebraic Geometry
2007-05-23 v2
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.
Cite
@article{arxiv.math/0306030,
title = {The Hodge theory of algebraic maps},
author = {Mark Andrea A. de Cataldo and Luca Migliorini},
journal= {arXiv preprint arXiv:math/0306030},
year = {2007}
}
Comments
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