دانلود کتاب Normal Surface Singularities

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Preface
Contents
1 Introduction
1.1 General Introduction
1.2 Why a New Book?
1.3 Examples and Constructions
1.4 Prologue of the Chapters
1.5 What Is New?
1.6 Organization of the Sections
1.7 What Is Not Covered
2 Resolution of Surface Singularities
2.1 Modifications and Resolutions
2.2 The Embedded Resolution Graph
2.2.A Continued Fraction and Dedekind Sums
2.3 Example: Hirzebruch–Jung Singularities
2.4 Existence and Uniqueness of the Minimal Resolution
2.5 Analytic Realizations: Theorems of Grauert and Winters
3 The Link
3.1 The Local Conic Structure of Isolated Analytic Germs. The Link
3.2 Embedded Links. Milnor Fibration
3.2.A The Homological Package of the Milnor Fibration
3.3 Plumbed 3-Manifolds: Plumbing Graphs
3.3.A The Plumbing Calculus
3.4 Homological Properties of the Link
3.5 Examples of Special Graphs
3.5.A Star-Shaped Graphs
3.5.B Cyclic Graphs
3.5.C Surgery 3-Manifolds
3.6 Basic Classification Theorems on 3-Manifolds and Links
3.7 The Fundamental Group of the Link
4 Coverings
4.1 Cyclic Coverings
4.1.A Cyclic Coverings of Graphs
4.1.B The Universal Covering of the Embedded Resolution Graph
4.1.C Ramified Cyclic Coverings of Germs
4.1.D Algebraic Monodromy and Cyclic Coverings
4.1.E o–Ramified Cyclic Coverings
4.2 Abelian Coverings
5 Examples
5.1 Weighted Homogeneous Singularities
5.2 Superisolated Singularities
5.3 Splice Diagrams
5.4 Splice Quotient Singularities
5.5 Newton Non-degenerate Singularities
5.5.A The Classical Case of Hypersurfaces in ps: [/EMC pdfmark [/Subtype /Span /ActualText (left parenthesis double struck upper C Superscript n plus 1 Baseline comma 0 right parenthesis) /StPNE pdfmark [/StBMC pdfmark(Cn+1,0)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
5.5.B Weil Divisors in Affine Toric Singularities
6 Invariants Associated with a Resolution
6.1 Local Divisor Class Group
6.1.A ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper Q) /StPNE pdfmark [/StBMC pdfmarkQps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Cartier Divisors and Canonical Coverings
6.2 Natural Line Bundles
6.3 The Canonical Cycle
6.3.A ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper Z Subscript upper K Superscript 2 Baseline plus StartAbsoluteValue script upper V EndAbsoluteValue) /StPNE pdfmark [/StBMC pdfmarkZK2+|V|ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Formulae
6.3.B The Gorenstein Property
6.4 Vanishing Theorems
6.4.A The Cohomological Cycle
6.5 Base Point Freeness
6.6 The Monoids ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S) /StPNE pdfmark [/StBMC pdfmarkSps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S prime) /StPNE pdfmark [/StBMC pdfmarkSps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
6.6.A The Representatives rh and sh
6.6.B The `Local\' Zariski Decomposition
6.7 The Monoids ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S Subscript a n) /StPNE pdfmark [/StBMC pdfmarkSanps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S prime Subscript a n) /StPNE pdfmark [/StBMC pdfmarkSanps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
6.7.A Kulikov Singularities
6.8 The (Equivariant) Geometric Genus and Laufer\'s Duality
6.8.A The Linear Subspace Arrangement ps: [/EMC pdfmark [/Subtype /Span /ActualText (left brace normal upper Omega Subscript upper X overTilde Baseline left parenthesis script upper I right parenthesis right brace Subscript script upper I subset of script upper V) /StPNE pdfmark [/StBMC pdfmark{ΩX\"0365X(I)}IVps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark of Forms
6.8.B A Topological Upper Bounds for pg. The Invariant Pathi
6.8.C A Topological Lower Bounds for pg
6.8.D Plurigenera
6.9 Relations with Smoothing Invariants
6.9.A The Formulae of Laufer, Durfee and Wahl
6.9.B Thom–Sebastiani Type Results and Suspension-Formulae
6.9.C Some Open Problems for Hypersurface Singularities
6.10 Spin and Spinc Structures
6.10.A Turaev\'s Euler Structures
7 The Artin–Laufer Program
7.1 Rational Singularities
7.1.A Some Analytic Invariants Described Topologically
7.1.B Some Invariants of the Universal Abelian Covering
7.2 Elliptic Singularities
7.2.A Elliptic Kulikov Singularities
7.2.B Minimally Elliptic Singularities
7.2.C The Elliptic Sequence, General Case
7.2.D The Elliptic Sequence, Numerically Gorenstein Case
7.2.E The `second\' Elliptic Sequence, General Case
7.2.F Maximally Elliptic Numerically Gorenstein Germs
7.2.G The Multiplicity and Hilbert–Samuel Function
7.2.H Non-maximally Elliptic Singularities
7.2.I The `generic\' Analytic Structure of Elliptic Singularities
7.3 Weighted Cubes and Generalized Computation Sequences
7.3.A The Topology of the Spaces {Sk,n}n. Deformation Retractions
7.3.B Measure of Non-rationality. `Bad\' Vertices
7.3.C Lattice Fibrations. Universal Cycles in the Fibers
7.3.D Concatenated Computation Sequences of AR Graphs
8 Multivariable Divisorial Filtration
8.1 Multi-Variable Series
8.1.A Multigradings
8.1.B Poincaré series of Weighted Homogeneous Singularities
8.1.C Filtrations
8.2 Divisorial Filtration and its Multivariable Series
8.2.A The Series H(t) and P(t)
8.3 Linear Subspace Arrangements Associated with the Filtration
8.4 The Topological Series Z(t)
8.4.A The Extension of Z(t) to the Grothendieck Ring
8.4.B Motivic Extension of Z(t) via the Space of Divisors
8.4.C ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper Z left parenthesis double struck upper L comma bold t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkZ(L,t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper P left parenthesis double struck upper L comma bold t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkP(L,t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark for Cusp Singularities
8.5 Singularities Satisfying the `end curve condition\'
8.5.A The Identity P(t)=Z(t) and the Monomial Filtration
8.5.B Topological Characterization of ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S prime Subscript a n) /StPNE pdfmark [/StBMC pdfmarkSanps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S Subscript a n) /StPNE pdfmark [/StBMC pdfmarkSanps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
8.5.C Base Points of ps: [/EMC pdfmark [/Subtype /Span /ActualText (phi Superscript asterisk Baseline German m Subscript upper X comma o) /StPNE pdfmark [/StBMC pdfmarkϕ*mX,ops: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and Multiplicity
8.5.D The Monomial Condition and End Curve Theorem
8.6 Reductions of Variables in the Series P(t) and Z(t)
8.6.A Examples. Is ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper P Subscript h comma script upper I) /StPNE pdfmark [/StBMC pdfmarkPh, Ips: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Topological/Combinatorial?
8.6.B Example. P0 and Z0 for Superisolated Singularities
8.6.C The Ring ps: [/EMC pdfmark [/Subtype /Span /ActualText (circled plus Subscript n greater than or equals 0 Baseline phi Subscript asterisk Baseline left parenthesis script upper O Subscript upper X overTilde Baseline left parenthesis minus n l right parenthesis right parenthesis Subscript o Baseline) /StPNE pdfmark [/StBMC pdfmarkn≥0 ϕ*(OX\"0365X(-nl))ops: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
8.7 The Periodic Constant of One-Variable Series
8.7.A Okuma\'s Additivity Formula
9 Topological Invariants. The Seiberg–Witten Invariant
9.1 The Casson Invariant
9.2 The Casson Invariant Conjecture of Neumann–Wahl
9.2.A The Proof of CIC for Splice Type Singularities
9.3 The Casson–Walker Invariant
9.3.A Additivity Formulae for λ and ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper K squared plus StartAbsoluteValue script upper V EndAbsoluteValue) /StPNE pdfmark [/StBMC pdfmarkK2+|V|ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
9.4 The Reidemeister–Turaev Torsion. Generalities
9.4.A The Fourier Transform
9.5 The Reidemeister–Turaev Torsion of Graph 3-Manifolds
9.5.A Additivity Formula for the Torsion
9.6 The Seiberg–Witten Invariant
9.6.A The Seiberg–Witten Invariant and the Series Z(t)
9.7 The Seiberg–Witten Invariant Conjecture/Coincidence
9.7.A SWIC for Weighted Homogeneous Singularities
9.7.B SWIC and Superisolated Singularities
9.7.C The Seiberg–Witten Invariant and Abelian Coverings
10 Ehrhart Theory and the Seiberg–Witten Invariant
10.1 Introduction into Ehrhart Theory
10.1.A Equivariant Multivariable Ehrhart Theory
10.2 Multivariable Rational Functions and Their Periodic Constants
10.3 Ehrhart Theory of Z(t) Associated with a Plumbing Graph
10.3.A Reduction of the Variables of Z(t)
10.3.B Technical Lemmas Regarding the Intersection Form
10.4 The Modified Counting Function
10.4.A Convexity Property of the Modified Counting Functions
10.4.B Additivity Formula for the Modified Counting Functions
10.5 General Additivity Formulae
10.6 Duality for the Topological Series
10.6.A The `Polynomial Part\' of the Series Z(t)
10.6.B Polytopes, Lattice Points and the Seiberg–Witten Invariant
11 Lattice Cohomology
11.1 The Lattice Cohomology Associated with a System of Weights
11.1.A The Lattice Cohomology Associated with a Plumbing Graph
11.1.B The Lattice Cohomology and the Seiberg–Witten Invariant
11.2 Graded Roots and Their Cohomologies
11.2.A The Graded Root Associated with a Plumbing Graph
11.3 Graded Roots of Almost Rational Graphs
11.3.A Example. Star-Shaped Graphs
11.3.B Example. The Surgery Manifold ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper S Subscript negative d Superscript 3 Baseline left parenthesis upper K right parenthesis) /StPNE pdfmark [/StBMC pdfmarkS3-d(K)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
11.3.C Superisolated Singularities with One Cusp
11.4 The Reduction Theorem
11.5 Application. ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H Superscript asterisk) /StPNE pdfmark [/StBMC pdfmarkH*ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark of the Surgery Manifold ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper S Subscript negative d Superscript 3 Baseline left parenthesis number sign Subscript i Baseline upper K Subscript i Baseline right parenthesis) /StPNE pdfmark [/StBMC pdfmarkS3-d(#iKi)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
11.5.A ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H Superscript 0 Baseline left parenthesis upper S Subscript negative d Superscript 3 Baseline left parenthesis number sign Subscript i Baseline upper K Subscript i Baseline right parenthesis right parenthesis) /StPNE pdfmark [/StBMC pdfmarkH0(S3-d(#iKi))ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and the Multiplicity Sequences
11.5.B Superisolated Singularities with More Cusps
11.6 Path Lattice Cohomology
11.6.A Lattice Cohomology of Newton Non-degenerateGerms
11.7 Lattice Cohomology and Heegaard Floer Homology
11.8 Combinatorial Lattice Cohomology with Special Weight Functions
11.9 Analytic Lattice Cohomology of Normal Surface Singularities
11.9.A Analytic Reduction Theorem
11.9.B Examples
11.9.C ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper H Subscript a n comma 0 Superscript asterisk) /StPNE pdfmark [/StBMC pdfmarkH*an,0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and pg–Constant Deformations
12 Appendix. Complex Analytic Spaces
12.1 Analytic Algebras
12.2 Complex Spaces
12.3 Analytic Coverings
12.4 Complex Reduced Surfaces
Bibliography
Index