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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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Additional Information

Mark Andrea A. de Cataldo
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: mde@math.sunysb.edu

Luca Migliorini
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Email: migliori@dm.unibo.it

DOI: https://doi.org/10.1090/S0273-0979-09-01260-9
Received by editor(s): December 16, 2007
Received by editor(s) in revised form: July 17, 2008, December 28, 2008, and February 13, 2009
Published electronically: June 26, 2009
Additional Notes: The second author was partially supported by GNSAGA and PRIN 2007 project “Spazi di moduli e teoria di Lie”
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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