Graduate Texts in Mathematics

Intersection Homology & Perverse Sheaves

with Applications to Singularities

Autoren: Maxim, Laurenţiu G.

Vorschau
  • 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
Weitere Vorteile

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eBook 24,60 €
50,28 € (Listenpreis)
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  • ISBN 978-3-030-27644-7
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Hardcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Über dieses Lehrbuch

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.


Über die Autor*innen

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.

Stimmen zum Buch

“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)


Inhaltsverzeichnis (12 Kapitel)

Inhaltsverzeichnis (12 Kapitel)
  • Topology of Singular Spaces: Motivation, Overview

    Seiten 1-9

    Maxim, Laurenţiu G.

  • Intersection Homology: Definition, Properties

    Seiten 11-36

    Maxim, Laurenţiu G.

  • L-Classes of Stratified Spaces

    Seiten 37-51

    Maxim, Laurenţiu G.

  • Brief Introduction to Sheaf Theory

    Seiten 53-80

    Maxim, Laurenţiu G.

  • Poincaré–Verdier Duality

    Seiten 81-92

    Maxim, Laurenţiu G.

Dieses Buch kaufen

eBook 24,60 €
50,28 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-030-27644-7
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
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Bibliografische Information

Bibliographic Information
Buchtitel
Intersection Homology & Perverse Sheaves
Buchuntertitel
with Applications to Singularities
Autoren
Titel der Buchreihe
Graduate Texts in Mathematics
Buchreihen Band
281
Copyright
2019
Verlag
Springer International Publishing
Copyright Inhaber
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
Buchreihen ISSN
0072-5285
Auflage
1
Seitenzahl
XV, 270
Anzahl der Bilder
136 schwarz-weiß Abbildungen
Themen