ENGLISH

Intersection Homology & Perverse Sheaves: with Applications to Singularities

By Laurenţiu G. Maxim

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-27643-0, 978-3-030-27644-7
Language
english
Format
PDF
Filesize
4 MB (3927965 bytes)
Series
Graduate Texts in Mathematics 281
Edition
1st ed. 2019
Pages
XV, 270\278
Time added
2020-02-08 04:41:39
Mathematics; Algebraic Topology; Algebraic Geometr

Description

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. Front Matter ....Pages i-xv Topology of Singular Spaces: Motivation, Overview (Laurenţiu G. Maxim)....Pages 1-9 Intersection Homology: Definition, Properties (Laurenţiu G. Maxim)....Pages 11-36 L-Classes of Stratified Spaces (Laurenţiu G. Maxim)....Pages 37-51 Brief Introduction to Sheaf Theory (Laurenţiu G. Maxim)....Pages 53-80 Poincaré–Verdier Duality (Laurenţiu G. Maxim)....Pages 81-92 Intersection Homology After Deligne (Laurenţiu G. Maxim)....Pages 93-116 Constructibility in Algebraic Geometry (Laurenţiu G. Maxim)....Pages 117-128 Perverse Sheaves (Laurenţiu G. Maxim)....Pages 129-148 The Decomposition Package and Applications (Laurenţiu G. Maxim)....Pages 149-179 Hypersurface Singularities. Nearby and Vanishing Cycles (Laurenţiu G. Maxim)....Pages 181-219 Overview of Saito’s Mixed Hodge Modules, and Immediate Applications (Laurenţiu G. Maxim)....Pages 221-244 Epilogue (Laurenţiu G. Maxim)....Pages 245-253 Back Matter ....Pages 255-270

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