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

By M. A. Cataldo, L. Migliorini. 2007

245 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5014e8d5126b2cdc5e089ae0de47eacdf2427071

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The perverse filtration and the Lefschetz Hyperplane Theorem (2008, methodology): “For a survey on the decomposition theorem, see [13].”
Hitchin fibrations, abelian surfaces, and the P=W conjecture (2019, unknown): “Some references are [7, 17, 19, 50].”
Singular Intersection Homology (2020, background): “As such, Hodge theory already appears and has an important role in some of the references we have already cited, including [68, 76, 163, 197].”
Enumeration of points, lines, planes, etc (2016, unknown): “ed Q‘-algebras B(M) Q Q‘’H 2(Y A ;Q‘): In general, the intersection cohomology IH (X;Q ‘)is a module over the cohomology H (X;Q‘), satisfying the Poincare duality and the hard Lefschetz theorems. See [dCM09] for an introduc-´ tion and precise statements. We obtain Theorem 6 from the following genera”