The Decomposition Theorem and the topology of algebraic maps

Details The Decomposition Theorem and the topology of algebraic maps The Decomposition Theorem and the topology of algebraic maps

2007-12-03

arxiv.org/abs/0712.0349v2

Mathematics

Algebraic Geometry

117 pages. New title. Major structure changes. Final version of a survey to appear in the Bulletin of the AMS

Scientific paper

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, indicate some important applications and examples.

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