The decomposition theorem, perverse sheaves and the topology of algebraic maps

de Cataldo, Mark; Migliorini, Luca

doi:10.1090/S0273-0979-09-01260-9

The decomposition theorem, perverse sheaves and the topology of algebraic maps

Authors: Mark Andrea A. de Cataldo and Luca Migliorini
Journal: Bull. Amer. Math. Soc. 46 (2009), 535-633
MSC (2000): Primary 14-02, 14C30, 14Dxx, 14Lxx, 18E30
DOI: https://doi.org/10.1090/S0273-0979-09-01260-9
Published electronically: June 26, 2009
MathSciNet review: 2525735
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Abstract: We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the decomposition theorem and indicate some important applications and examples.

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