Resolution of Curve and Surface Singularities in Characteristic Zero - nieuw boek

EAN (ISBN-13): 9781402020292
Verschijningsjaar: 2012
Uitgever: Springer Netherlands

Boek bevindt zich in het datenbestand sinds 2017-05-11T00:16:33+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2023-09-23T12:50:22+02:00 (Amsterdam)
ISBN/EAN: 9781402020292

ISBN - alternatieve schrijfwijzen:
978-1-4020-2029-2
alternatieve schrijfwijzen en verwante zoekwoorden:
Titel van het boek: singularities

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Gegevens van de uitgever

Auteur: K. Kiyek
Titel: Algebras and Applications; Resolution of Curve and Surface Singularities in Characteristic Zero
Uitgeverij: Springer; Springer Netherland
486 Bladzijden
Verschijningsjaar: 2012-09-11
Dordrecht; NL
Taal: Engels
55,00 € (DE)

EA; E107; eBook; Nonbooks, PBS / Mathematik/Arithmetik, Algebra; Algebraische Geometrie; Verstehen; Abelian group; Blowing up; Dimension; Divisor; Grad; algebraic geometry; brandonwiskunde; commutative algebra; C; Algebraic Geometry; Commutative Rings and Algebras; Field Theory and Polynomials; Several Complex Variables and Analytic Spaces; Mathematics and Statistics; Algebra; Komplexe Analysis, komplexe Variablen, Funktionentheorie; BB

I Valuation Theory.- 1 Marot Rings.- 2 Manis Valuation Rings.- 3 Valuation Rings and Valuations.- 4 The Approximation Theorem For Independent Valuations.- 5 Extensions of Valuations.- 6 Extending Valuations to Algebraic Overfields.- 7 Extensions of Discrete Valuations.- 8 Ramification Theory of Valuations.- 9 Extending Valuations to Non-Algebraic Overfields.- 10 Valuations of Algebraic Function Fields.- 11 Valuations Dominating a Local Domain.- II One-Dimensional Semilocal Cohen-Macaulay Rings.- 1 Transversal Elements.- 2 Integral Closure of One-Dimensional Semilocal Cohen-Macaulay Rings.- 3 One-Dimensional Analytically Unramified and Analytically Irreducible CM-Rings.- 4 Blowing up Ideals.- 5 Infinitely Near Rings.- III Differential Modules and Ramification.- 1 Introduction.- 2 Norms and Traces.- 3 Formally Unramified and Unramified Extensions.- 4 Unramified Extensions and Discriminants.- 5 Ramification For Quasilocal Rings.- 6 Integral Closure and Completion.- IV Formal and Convergent Power Series Rings.- 1 Formal Power Series Rings.- 2 Convergent Power Series Rings.- 3 Weierstraß Preparation Theorem.- 4 The Category of Formal and Analytic Algebras.- 5 Extensions of Formal and Analytic Algebras.- V Quasiordinary Singularities.- 1 Fractionary Power Series.- 2 The Jung-Abhyankar Theorem: Formal Case.- 3 The Jung-Abhyankar Theorem: Analytic Case.- 4 Quasiordinary Power Series.- 5 A Generalized Newton Algorithm.- 6 Strictly Generated Semigroups.- VI The Singularity Zq = XYp.- 1 Hirzebruch-Jung Singularities.- 2 Semigroups and Semigroup Rings.- 3 Continued Fractions.- 4 Two-Dimensional Cones.- 5 Resolution of Singularities.- VII Two-Dimensional Regular Local Rings.- 1 Ideal Transform.- 2 Quadratic Transforms and Ideal Transforms.- 3 Complete Ideals.- 4 Factorization ofComplete Ideals.- 5 The Predecessors of a Simple Ideal.- 6 The Quadratic Sequence.- 7 Proximity.- 8 Resolution of Embedded Curves.- VIII Resolution of Singularities.- 1 Blowing up Curve Singularities.- 2 Resolution of Surface Singularities I: Jung’s Method.- 3 Quadratic Dilatations.- 4 Quadratic Dilatations of Two-Dimensional Regular Local Rings.- 5 Valuations of Algebraic Function Fields in Two Variables.- 6 Uniformization.- 7 Resolution of Surface Singularities II: Blowing up and Normalizing.- Appendices.- A Results from Classical Algebraic Geometry.- 1 Generalities.- 1.1 Ideals and Varieties.- 1.2 Rational Functions and Maps.- 1.3 Coordinate Ring and Local Rings.- 1.4 Dominant Morphisms and Closed Embeddings.- 1.5 Elementary Open Sets.- 1.6 Varieties as Topological Spaces.- 1.7 Local Ring on a Subvariety.- 2 Affine and Finite Morphisms.- 3 Products.- 4 Proper Morphisms.- 4.1 Space of Irreducible Closed Subsets.- 4.3 Proper Morphisms.- 5 Algebraic Cones and Projective Varieties.- 6 Regular and Singular Points.- 7 Normalization of a Variety.- 8 Desingularization of a Variety.- 9 Dimension of Fibres.- 10 Quasifinite Morphisms and Ramification.- 10.1 Quasifinite Morphisms.- 10.2 Ramification.- 11 Divisors.- 12 Some Results on Projections.- 13 Blowing up.- 14 Blowing up: The Local Rings.- B Miscellaneous Results.- 1 Ordered Abelian Groups.- 1.1 Isolated Subgroups.- 1.2 Initial Index.- 1.3 Archimedean Ordered Groups.- 1.4 The Rational Rank of an Abelian Group.- 2 Localization.- 3 Integral Extensions.- 4 Some Results on Graded Rings and Modules.- 4.1 Generalities.- 4.3 Homogeneous Localization.- 4.4 Integral Closure of Graded Rings.- 5 Properties of the Rees Ring.- 6 Integral Closure of Ideals.- 6.1 Generalities.- 6.2 Integral Closure of Ideals.- 6.3 Integral Closure ofIdeals and Valuation Theory.- 7 Decomposition Group and Inertia Group.- 8 Decomposable Rings.- 9 The Dimension Formula.- 10 Miscellaneous Results.- 10.1 The Chinese Remainder Theorem.- 10.2 Separable Noether Normalization.- 10.3 The Segre Ideal.- 10.4 Adjoining an Indeterminate.- 10.5 Divisor Group and Class Group.- 10.6 Calculating a Multiplicity.- 10.7 A Length Formula.- 10.8 Quasifinite Modules.- 10.9 Maximal Primary Ideals.- 10.10 Primary Decomposition in Non-Noetherian Rings.- 10.11 Discriminant of a Polynomial.- Index of Symbols.