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000857582 020__ $$a9783030033507$$q(electronic book)
000857582 020__ $$a3030033503$$q(electronic book)
000857582 020__ $$z9783030033491
000857582 035__ $$aSP(OCoLC)on1080520568
000857582 035__ $$aSP(OCoLC)1080520568
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000857582 050_4 $$aQA565
000857582 08204 $$a516.352$$223
000857582 24500 $$aSingular algebraic curves :$$bwith an appendix by Oleg Viro /$$cGert-Martin Greuel, Christoph Lossen and Eugenii Shustin.
000857582 264_1 $$aCham :$$bSpringer,$$c2018.
000857582 300__ $$a1 online resource.
000857582 336__ $$atext$$btxt$$2rdacontent
000857582 337__ $$acomputer$$bc$$2rdamedia
000857582 338__ $$aonline resource$$bcr$$2rdacarrier
000857582 4901_ $$aSpringer monographs in mathematics
000857582 5050_ $$aIntro; Preface; Acknowledgements; References; Contents; Notations and Conventions; References; 1 Zero-Dimensional Schemes for Singularities; 1.1 Cluster and Zero-Dimensional Schemes; 1.1.1 Constellations and Cluster; 1.1.2 Cluster Schemes and Equisingularity; 1.1.3 The Hilbert Scheme of Cluster Schemes; 1.1.4 Zero-Dimensional Schemes for Analytic Types; 1.2 Non-classical Singularity Invariants; 1.2.1 Determinacy Bounds; 1.2.2 New Topological Invariants; 1.2.3 New Analytic Invariants; 1.3 Historical Notes and References; References; 2 Global Deformation Theory; 2.1 Classical Global Theorems
000857582 5058_ $$a2.1.1 Divisors and Linear Systems2.1.2 Bézout's Theorem; 2.1.3 Bertini's and Noether's Theorems; 2.1.4 Polar and Dual Curves; 2.2 Equisingular Families of Singular Algebraic Varieties; 2.2.1 Families with Imposed Conditions on Singularities; 2.2.2 Hilbert Schemes of Singular Hypersurfaces; 2.2.3 T-Smooth Families of Isolated Hypersurface Singularities; 2.3 Construction via Deformation; 2.3.1 General Idea of the Patchworking Construction; 2.3.2 Polytopes and calS-transversality; 2.3.3 Gluing Singular Hypersurfaces; 2.3.4 SQH and NND Isolated Hypersurface Singularities
000857582 5058_ $$a2.3.5 Lower Deformations of Hypersurface Singularities2.3.6 Cohomology Vanishing Conditions; 2.4 Appendix: The Patchworking Construction; 2.4.1 Elements of Toric Geometry; 2.4.2 Viro's Theorem for Hypersurfaces; 2.4.3 Viro's Method in Real Algebraic Geometry; 2.4.4 Viro's Theorem for Complete Intersections; 2.4.5 Other Examples of Patchworking; 2.5 Historical Notes and References; References; 3 H1-Vanishing Theorems; 3.1 Riemann-Roch Type H1-Vanishing; 3.2 Applications of Kodaira Vanishing; 3.3 Reider-Bogomolov Theory; 3.4 The Horace Method; 3.4.1 The Basic Horace Method
000857582 5058_ $$a3.4.2 Applications of the Basic Horace Method3.4.3 Variations of the Horace Method; 3.5 The Castelnuovo Function; 3.6 H1-Vanishing for Generic Zero-Dimensional Schemes; 3.7 Historical Notes and References; References; 4 Equisingular Families of Curves; 4.1 Overview of New Results and Methods; 4.1.1 Nonemptiness; 4.1.2 T-Smoothness and Deformation Completeness; 4.1.3 Irreducibility; 4.1.4 Comments on the Methods; 4.2 Formulation of Problems, Discussion of Results, Examples; 4.2.1 Statement of the Problem; 4.2.2 Curves with Nodes and Cusps: from Severi to Harris
000857582 5058_ $$a4.2.3 Examples of Obstructed and Reducible ESF4.3 T-Smoothness; 4.3.1 Linear Conditions; 4.3.2 Quadratic Conditions; 4.3.3 Obstructed Equisingular Families; 4.3.4 ESF of Hypersurfaces in mathbbPn; 4.4 Independence of Simultaneous Deformations; 4.4.1 Joint Versal Deformations; 4.4.2 1-Parametric Deformations; 4.5 Existence; 4.5.1 Conditions for the Patchworking Construction; 4.5.2 Plane Curves with Nodes and Cusps; 4.5.3 Curves and Hypersurfaces with Simple Singularities; 4.5.4 Hypersurfaces with Arbitrary Singularities; 4.5.5 Plane Curves with Arbitrary Singularities
000857582 506__ $$aAccess limited to authorized users.
000857582 588__ $$aOnline resource; title from PDF title page (viewed January 2, 2019)
000857582 650_0 $$aCurves, Algebraic.
000857582 7001_ $$aGreuel, G.-M.$$q(Gert-Martin),$$eeditor.
000857582 7001_ $$aLossen, Christoph,$$eeditor.
000857582 7001_ $$aShustin, Eugenii,$$eeditor.
000857582 830_0 $$aSpringer monographs in mathematics.
000857582 852__ $$bebk
000857582 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-03350-7$$zOnline Access$$91397441.1
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000857582 980__ $$aBIB
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