Buch, Englisch, Band 281, 270 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 441 g
with Applications to Singularities
Buch, Englisch, Band 281, 270 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 441 g
Reihe: Graduate Texts in Mathematics
ISBN: 978-3-030-27646-1
Verlag: Springer International Publishing
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.