The Hodge theory of algebraic maps

2003/06/02 by Mark Andrea A. de Cataldo, de Cataldo, Mark Andrea A., Luca Migliorini +1 · 3 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0306030

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

arxiv created 2004/05/24 · arxiv updated 2009/11/30

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.

Cited by

• Cohomology of compactified Jacobians for locally planar integral curves
• A decomposition theorem for Lefschetz modules
• A non-holomorphic P=W phenomenon

Related

• Hodge-theoretic aspects of the Decomposition Theorem
• The Hodge theory of the Decomposition Theorem (after de Cataldo and Migliorini)
• Partial Cohomologically Complete Intersections via Hodge Theory
• The Decomposition Theorem and the Intersection Cohomology of Quotients in Algebraic Geometry
• Mixed Hodge Structures