LEADER 04103nam 22005895 450 001 9910360849503321 005 20251113195200.0 010 $a3-030-27644-9 024 7 $a10.1007/978-3-030-27644-7 035 $a(CKB)4100000009939748 035 $a(MiAaPQ)EBC5987610 035 $a(DE-He213)978-3-030-27644-7 035 $a(PPN)248599089 035 $a(EXLCZ)994100000009939748 100 $a20191130d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntersection Homology & Perverse Sheaves $ewith Applications to Singularities /$fby Lauren?iu G. Maxim 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (278 pages) $cillustrations 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v281 311 08$a3-030-27643-0 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson?Bernstein?Deligne?Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito?s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v281 606 $aAlgebraic topology 606 $aAlgebraic geometry 606 $aFunctions of complex variables 606 $aAlgebraic Topology 606 $aAlgebraic Geometry 606 $aSeveral Complex Variables and Analytic Spaces 615 0$aAlgebraic topology. 615 0$aAlgebraic geometry. 615 0$aFunctions of complex variables. 615 14$aAlgebraic Topology. 615 24$aAlgebraic Geometry. 615 24$aSeveral Complex Variables and Analytic Spaces. 676 $a514.23 676 $a514.23 700 $aMaxim$b Laurent?iu G.$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781353 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360849503321 996 $aIntersection Homology & Perverse Sheaves$91732514 997 $aUNINA