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Graduate Texts in Mathematics

Intersection Homology & Perverse Sheaves

with Applications to Singularities

Authors: Maxim, Laurenţiu G.

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  • 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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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-030-27644-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • Due: December 26, 2019
  • ISBN 978-3-030-27643-0
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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

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.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-030-27644-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • Due: December 26, 2019
  • ISBN 978-3-030-27643-0
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Intersection Homology & Perverse Sheaves
Book Subtitle
with Applications to Singularities
Authors
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
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XV, 270
Number of Illustrations
136 b/w illustrations
Topics