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  • Produktbild: Resolution of Curve and Surface Singularities in Characteristic Zero
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Resolution of Curve and Surface Singularities in Characteristic Zero

Aus der Reihe Algebra and Applications

48,99 €

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From the reviews:



"As indicated in the title … describes different methods of resolution of singularities of curves and surfaces … . The first seven chapters are dedicated to developing the material … . The two appendixes, on algebraic geometry and commutative algebra, contain generalities and classical results needed in the previous chapters. This completes one of the aims of the authors: To write a book as self-contained as possible. ... In conclusion, the book is an interesting exposition of resolution of singularities in low dimensions … ." (Ana Bravo, Mathematical Reviews, 2005e)


"The monograph presents a modern theory of resolution of isolated singularities of algebraic curves and surfaces over algebraically closed fields of characteristic zero. … The exposition is self-contained and is supplied by an appendix, covering some classical algebraic geometry and commutative algebra." (Eugenii I. Shustin, Zentralblatt MATH, Vol. 1069 (20), 2005)

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

05.12.2010

Abbildungen

XXII, 486 p.

Verlag

Springer Netherland

Seitenzahl

486

Maße (L/B/H)

23,5/15,5/2,8 cm

Gewicht

762 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-90-481-6573-5

Rezension

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

05.12.2010

Abbildungen

XXII, 486 p.

Verlag

Springer Netherland

Seitenzahl

486

Maße (L/B/H)

23,5/15,5/2,8 cm

Gewicht

762 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-90-481-6573-5

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Resolution of Curve and Surface Singularities in Characteristic Zero
  • Produktbild: Resolution of Curve and Surface Singularities in Characteristic Zero
  • 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.