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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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The decomposition theorem, perverse sheaves and the topology of algebraic maps
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by Mark Andrea A. de Cataldo and Luca Migliorini PDF
Bull. Amer. Math. Soc. 46 (2009), 535-633 Request permission


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:
  • Luca Migliorini
  • Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
  • MR Author ID: 248786
  • ORCID: 0000-0001-5145-0755
  • Email:
  • 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”
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 46 (2009), 535-633
  • MSC (2000): Primary 14-02, 14C30, 14Dxx, 14Lxx, 18E30
  • DOI:
  • MathSciNet review: 2525735