Degeneration of Kähler manifolds

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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“…8.1, was proved by P. Deligne in [62]. For Hodge-theoretic approaches to the local case, see [40,168,73,96]. The "singular" case, i.e.…”

Section: Historical and Other Remarksmentioning

confidence: 98%

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

Andrea

Migliorini

2009

Bull. Amer. Math. Soc.

162

152

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“…Then the local invariant cycle theorem [3] tells that the image of the map induced by the restriction from a small tubular neighbourhood…”

Section: Example 34mentioning

confidence: 99%

On the geometry of regular maps from a quasi-projective surface to a curve

Parameswaran

Tibăr

2015

European Journal of Mathematics

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“…8.1, was proved by P. Deligne in [62]. For Hodge-theoretic approaches to the local case, see [40,168,73,96]. The "singular" case, i.e., Theorem 1.7.1, is proved in [9], p.164; see also [156].…”

Section: A Few Examplesmentioning

confidence: 99%

Untitled

2009

Bull. Amer. Math. Soc.

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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.

show abstract

Degeneration of Kähler manifolds

Cited by 162 publications

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

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

On the geometry of regular maps from a quasi-projective surface to a curve

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