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Intersection Homology & Perverse Sheaves

with Applications to Singularities

  • Laurenţiu G. Maxim
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 281)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Laurenţiu G. Maxim
    Pages 11-36
  3. Laurenţiu G. Maxim
    Pages 37-51
  4. Laurenţiu G. Maxim
    Pages 53-80
  5. Laurenţiu G. Maxim
    Pages 81-92
  6. Laurenţiu G. Maxim
    Pages 93-116
  7. Laurenţiu G. Maxim
    Pages 117-128
  8. Laurenţiu G. Maxim
    Pages 129-148
  9. Laurenţiu G. Maxim
    Pages 149-179
  10. Laurenţiu G. Maxim
    Pages 245-253
  11. Back Matter
    Pages 255-270

About this book

Introduction

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.

Keywords

intersection homology introduction to intersection homology intersection homology examples Poincaré duality in singular spaces constructible sheaf perverse sheaf mixed Hodge module Kähler package BBDG decomposition theorem Saito's theory of mixed Hodge modules decomposition package applications of perverse sheaves to hypersurface singularities

Authors and affiliations

  • Laurenţiu G. Maxim
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin–MadisonMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-27644-7
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-27643-0
  • Online ISBN 978-3-030-27644-7
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site