Intersection Homology & Perverse Sheaves

with Applications to Singularities

Inbunden, Engelska, 2019

Av Laurenţiu G. Maxim, Laurentiu G. Maxim, Laurenţiu G. Maxim, Lauren¿iu G. Maxim

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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.

Produktinformation

Utgivningsdatum2019-12-10
Mått155 x 235 x 23 mm
Vikt558 g
FormatInbunden
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor270
FörlagSpringer Nature Switzerland AG
ISBN9783030276430

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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.

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.

“This is quite a lot for a relatively short book! … this book provides a great jumping-off point for the reader who wants to learn about these tools by a route leading to the forefront of modern research via lots of concrete geometric examples.” (Greg Friedman, Mathematical Reviews, March, 2023)“This book is a welcome addition to the family of introductions to intersection cohomology and perverse sheaves. … the author takes care to introduce and motivate the main objects of study with geometric examples. There are also regular exercises which will help readers come to grips with the material. … this book will ... be a very useful resource … .” (Jon Woolf, zbMATH 1476.55001, 2022)“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)