Intersection Homology & Perverse Sheaves
Springer International Publishing (Verlag)
978-3-030-27643-0 (ISBN)
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.
Laurentiu 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.
lt;p>"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)
Erscheinungsdatum | 12.12.2019 |
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Reihe/Serie | Graduate Texts in Mathematics |
Zusatzinfo | XV, 270 p. 136 illus. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 589 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Schlagworte | applications of perverse sheaves to hypersurface s • applications of perverse sheaves to hypersurface singularities • BBDG decomposition theorem • constructible sheaf • decomposition package • decomposition theorem • Intersection Homology • intersection homology examples • introduction to intersection homology • Kähler package • Kähler package • mixed Hodge module • perverse sheaf • Poincaré duality in singular spaces • Poincaré duality • Poincaré duality in singular spaces • Saito's theory of mixed Hodge modules • singular space |
ISBN-10 | 3-030-27643-0 / 3030276430 |
ISBN-13 | 978-3-030-27643-0 / 9783030276430 |
Zustand | Neuware |
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