Intersection Homology & Perverse Sheaves : with Applications to Singularities / by Laurenţiu G. Maxim.

Format:

Book

Author/Creator:

Maxim, Laurenţiu G., author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Graduate texts in mathematics 0072-5285 ; 281.

Graduate Texts in Mathematics, 0072-5285 ; 281

Language:

English

Subjects (All):

Algebraic topology.

Geometry, Algebraic.

Functions of complex variables.

Algebraic Topology.

Algebraic Geometry.

Several Complex Variables and Analytic Spaces.

Local Subjects:

Algebraic Topology.

Algebraic Geometry.

Several Complex Variables and Analytic Spaces.

Physical Description:

1 online resource (XV, 270 pages) : 136 illustrations.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson-Bernstein-Deligne-Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito's deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology and Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Contents:

Preface

1. Topology of singular spaces: motivation, overview

2. Intersection Homology: definition, properties

3. L-classes of stratified spaces

4. Brief introduction to sheaf theory

5. Poincaré-Verdier Duality

6. Intersection homology after Deligne

7. Constructibility in algebraic geometry

8. Perverse sheaves

9. The Decomposition Package and Applications

10. Hypersurface singularities. Nearby and vanishing cycles

11. Overview of Saito's mixed Hodge modules, and immediate applications

12. Epilogue

Bibliography

Index.

Other Format:

Printed edition:

ISBN:

978-3-030-27644-7

9783030276447

OCLC:

1129404775

Access Restriction:

Restricted for use by site license.