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The Decomposition Theorem and the topology of algebraic maps
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.Comment: 117 pages. New title. Major structure changes. Final version of a
survey to appear in the Bulletin of the AM
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