The Hodge Theory of algebraic maps

Mark Andrea A. de Cataldo; Luca Migliorini

doi:10.1016/j.ansens.2005.07.001

The Hodge Theory of algebraic maps

Mark Andrea A. de Cataldo
, Luca Migliorini

Mathematics

University of Bologna

Research output: Contribution to journal › Article › peer-review

82 Scopus citations

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.

Original language	English
Pages (from-to)	693-750
Number of pages	58
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	38
Issue number	5
DOIs	https://doi.org/10.1016/j.ansens.2005.07.001
State	Published - Sep 2005

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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.",

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AB - 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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SN - 0012-9593

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

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ER -

The Hodge Theory of algebraic maps

Abstract

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