Intersection Homology & Perverse Sheaves with Applications to Singularities /

• Main Author: Maxim, Laurenţiu G. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Graduate Texts in Mathematics, 281
• Subjects: Algebraic topology.; Algebraic geometry.; Functions of complex variables.; Algebraic Topology.; Algebraic Geometry.; Several Complex Variables and Analytic Spaces.

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 to...

Table of Contents:

• 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.