LEADER 04991nam 22006135 450 001 9910616394003321 005 20251223190040.0 010 $a9783031067532$b(electronic bk.) 010 $z9783031067525 024 7 $a10.1007/978-3-031-06753-2 035 $a(MiAaPQ)EBC7107718 035 $a(Au-PeEL)EBL7107718 035 $a(CKB)25048787000041 035 $a(PPN)265856361 035 $a(BIP)85932569 035 $a(BIP)83996163 035 $a(DE-He213)978-3-031-06753-2 035 $a(EXLCZ)9925048787000041 100 $a20221007d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNormal Surface Singularities /$fby András Némethi 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (732 pages) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x2197-5655 ;$v74 311 08$aPrint version: Némethi, András Normal Surface Singularities Cham : Springer International Publishing AG,c2022 9783031067525 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- 2 Resolution of Surface Singularities -- 3 The Link -- 4 Coverings -- 5 Examples -- 6 Invariants Associated With a Resolution -- 7 The Artin?Laufer Program -- 8 Multivariable Divisorial Filtration -- 9 Topological Invariants. The Seiberg?Witten Invariant -- 10 Ehrhart Theory and the Seiberg?Witten Invariant -- 11 Lattice Cohomology -- 12 Appendix. Complex Analytic Spaces -- References -- Index. 330 $aThis monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg?Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert?Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(?Walker) and Seiberg?Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg?Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x2197-5655 ;$v74 606 $aGeometry, Algebraic 606 $aFunctions of complex variables 606 $aAlgebraic topology 606 $aAlgebraic Geometry 606 $aSeveral Complex Variables and Analytic Spaces 606 $aAlgebraic Topology 615 0$aGeometry, Algebraic. 615 0$aFunctions of complex variables. 615 0$aAlgebraic topology. 615 14$aAlgebraic Geometry. 615 24$aSeveral Complex Variables and Analytic Spaces. 615 24$aAlgebraic Topology. 676 $a516.35 700 $aNe?methi$b Andra?s$0477395 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910616394003321 996 $aNormal Surface Singularities$92929622 997 $aUNINA