Intersection Homology & Perverse Sheaves
with Applications to Singularities
Authors: Maxim, Laurenţiu G.
Free Preview- Offers a taste of the main topics in the field through concrete examples and geometric applications
- Motivates further specialized study by building context and familiarity with examples
- Suits graduate students with only a basic background in topology and algebraic geometry
- Provides comprehensive references throughout to help readers navigate classic and recent literature
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- About this Textbook
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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 & 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.
- About the authors
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Laurenţiu G. Maxim is Professor of Mathematics at University of Wisconsin–Madison and a Researcher at the Institute of Mathematics of the Romanian Academy. His research interests lie at the interface of geometric topology and algebraic geometry, with an emphasis on the topological study of complex algebraic varieties. He has taught courses on intersection homology, perverse sheaves and their applications to singularity theory in the United States, Romania, Mainland China, and Hong Kong SAR.
- Reviews
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“This is a good textbook to prepare a student to delve into the current literature, and also a good reference for a researcher. A mathematician whose research or interest has come in contact with these topics would also find this a stimulating read on the subject.” (MAA Reviews, April 7, 2020)
- Table of contents (12 chapters)
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Topology of Singular Spaces: Motivation, Overview
Pages 1-9
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Intersection Homology: Definition, Properties
Pages 11-36
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L-Classes of Stratified Spaces
Pages 37-51
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Brief Introduction to Sheaf Theory
Pages 53-80
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Poincaré–Verdier Duality
Pages 81-92
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Intersection Homology & Perverse Sheaves
- Book Subtitle
- with Applications to Singularities
- Authors
-
- Laurenţiu G. Maxim
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 281
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-27644-7
- DOI
- 10.1007/978-3-030-27644-7
- Hardcover ISBN
- 978-3-030-27643-0
- Softcover ISBN
- 978-3-030-27646-1
- Series ISSN
- 0072-5285
- Edition Number
- 1
- Number of Pages
- XV, 270
- Number of Illustrations
- 136 b/w illustrations
- Topics
