Intersection Homology & Perverse Sheaves, 1st ed. 2019 with Applications to Singularities Graduate Texts in Mathematics Series, Vol. 281
Auteur : Maxim Laurenţiu G.
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 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.
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.
Date de parution : 12-2020
Ouvrage de 270 p.
15.5x23.5 cm
Date de parution : 12-2019
Ouvrage de 270 p.
15.5x23.5 cm
Mots-clés :
intersection homology; introduction to intersection homology; intersection homology examples; Poincaré duality in singular spaces; constructible sheaf; perverse sheaf; mixed Hodge module; Kähler package; BBDG decomposition theorem; Saito's theory of mixed Hodge modules; decomposition package; applications of perverse sheaves to hypersurface singularities
