LEADER 04636nam 22006735 450 001 9910747591903321 005 20240701172941.0 010 $a3-031-31925-7 024 7 $a10.1007/978-3-031-31925-9 035 $a(MiAaPQ)EBC30774820 035 $a(Au-PeEL)EBL30774820 035 $a(DE-He213)978-3-031-31925-9 035 $a(PPN)272918695 035 $a(CKB)28478158200041 035 $a(EXLCZ)9928478158200041 100 $a20231007d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHandbook of Geometry and Topology of Singularities IV /$fedited by José Luis Cisneros-Molina, Lę D?ng Tráng, José Seade 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (622 pages) 311 08$aPrint version: Cisneros-Molina, José Luis Handbook of Geometry and Topology of Singularities IV Cham : Springer International Publishing AG,c2023 9783031319242 327 $a1 Lę D?ng Tráng and Bernard Teissier, Limits of tangents, Whitney stratifications and a Plücker type formula -- 2 Anne Frühbis-Krüger and Matthias Zach, Determinantal singularities -- 3 Shihoko Ishii, Singularities, the space of arcs and applications to birational geometry -- 4 Hussein Mourtada, Jet schemes and their applications in singularities, toric resolutions and integer partitions -- 5 Wolfgang Ebeling and Sabir M. Gusein-Zade, Indices of vector fields and 1-forms -- 6 Shoji Yokura, Motivic Hirzebruch class and related topics -- 7 Guillaume Valette, Regular vectors and bi-Lipschitz trivial stratifications in o-minimal structures -- 8 Lev Birbrair and Andrei Gabrielov, Lipschitz Geometry of Real Semialgebraic Surfaces -- 9 Alexandre Fernandes and José Edson Sampaio, Bi-Lipschitz invariance of the multiplicity -- 10 Lorenzo Fantini and Anne Pichon, On Lipschitz Normally Embedded singularities -- 11 Ana Bravo and Santiago Encinas, Hilbert-Samuel multiplicity and finite projections -- 12 Francisco J. Castro-Jiménez, David Mond and Luis Narváez-Macarro, Logarithmic Comparison Theorems. 330 $aThis is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook. 606 $aTopology 606 $aAlgebraic geometry 606 $aMathematical analysis 606 $aTopology 606 $aAlgebraic Geometry 606 $aAnalysis 606 $aSingularitats (Matemŕtica)$2thub 606 $aGeometria algebraica$2thub 606 $aGrups topolňgics$2thub 608 $aLlibres electrňnics$2thub 615 0$aTopology. 615 0$aAlgebraic geometry. 615 0$aMathematical analysis. 615 14$aTopology. 615 24$aAlgebraic Geometry. 615 24$aAnalysis. 615 7$aSingularitats (Matemŕtica) 615 7$aGeometria algebraica 615 7$aGrups topolňgics 676 $a516.35 676 $a516.35 700 $aCisneros-Molina$b José Luis$01431728 701 $aD?ng Tráng$b Lę$01431729 701 $aSeade$b José$0368369 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910747591903321 996 $aHandbook of Geometry and Topology of Singularities IV$93574632 997 $aUNINA