Intersection Homology & Perverse Sheaves : with Applications to Singularities

2019 ed.

by Laurentiu G. Maxim

Book Details

Format Hardback or Cased Book

Book Series Graduate Texts in Mathematics

ISBN-10 3030276430

ISBN-13 9783030276430

Edition 2019 ed.

Publisher Springer Nature Switzerland AG

Imprint Springer Nature Switzerland AG

Country of Manufacture CH

Country of Publication GB

Publication Date Dec 10th, 2019

Print length 270 Pages

Weight 558 grams

Dimensions 24.00 x 15.30 x 2.30 cms

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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.

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.

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