Intersection Homology & Perverse Sheaves

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Beschreibung

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 Saitös 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 den Autor

Lauren¿iu 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.

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- 1. Topology of singular spaces: motivation, overview.- 2. Intersection Homology: definition, properties.- 3. L-classes of stratified spaces.- 4. Brief introduction to sheaf theory.- 5. Poincaré-Verdier Duality.- 6. Intersection homology after Deligne.- 7. Constructibility in algebraic geometry.- 8. Perverse sheaves.- 9. The Decomposition Package and Applications.- 10. Hypersurface singularities. Nearby and vanishing cycles.- 11. Overview of Saito's mixed Hodge modules, and immediate applications.- 12. Epilogue.- Bibliography.- Index.

Details

Erscheinungsjahr:	2019
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	288
Reihe:	Graduate Texts in Mathematics
Inhalt:	xv 270 S. 136 s/w Illustr. 270 p. 136 illus.
ISBN-13:	9783030276430
ISBN-10:	3030276430
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Maxim, Lauren¿iu G.
Auflage:	1st ed. 2019
Hersteller:	Springer International Publishing Graduate Texts in Mathematics
Maße:	241 x 160 x 22 mm
Von/Mit:	Lauren¿iu G. Maxim
Erscheinungsdatum:	10.12.2019
Gewicht:	0,6 kg

preigu-id: 116916942