skip to content
Resolution of curve and surface singularities in characteristic zero : in characteristic zero Preview this item
ClosePreview this item

Resolution of curve and surface singularities in characteristic zero : in characteristic zero

Author: Karl-Heinz Kiyek; José Luis Vicente Córdoba
Publisher: Boston : Kluwer Academic, 2004.
Series: Algebra and applications, 4.
Edition/Format:   Book : EnglishView all editions and formats

Covers the theory of resolutions of surface singularities in characteristic zero. This book presents two proofs for the existence of such resolutions. It also uses the uniformization of  Read more...


(not yet rated) 0 with reviews - Be the first.

More like this


Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...


Document Type: Book
All Authors / Contributors: Karl-Heinz Kiyek; José Luis Vicente Córdoba
ISBN: 1402020287 9781402020285
OCLC Number: 492703282
Description: 1 vol. (XXI-483 p.) ; 24 cm.
Contents: Preface. Note to the Reader. Terminology. I: Valuation Theory. 1. Marot Rings. 2. Manis Valuation Rings. 3. Valuation Rings and Valuations. 4. The Approximate 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 Ramified 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 Factions. 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 of Complete Ideals. 5. The Predecessors of a Simple Ideal. 6. Uniformization. 7. Resolution of Surface Singularities II: Blowing up and Normalizing. Appendices. A: Results from Classical Algebraic Geometry. 1. Generalities. 2. Affine and Finite Morphisms. 3. Products. 4. 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. 11. Divisors. 12. Some Results on Projections. 13. Blowing up. 14. Blowing up: the Local Rings. B: Miscellaneous Results. 1. Ordered Abelian Groups. 2. Localization. 3. Integral Extensions. 4. Some Results on Graded Rings and Modules. 5. Properties of the Rees Ring. 6. Integral Closure of Ideals. 7. Decomposition Group and Inertia Group. 8. Decomposable Rings. 9.
Series Title: Algebra and applications, 4.
Responsibility: K. Kiyek and J. L. Vicente.
More information:


Editorial reviews

Publisher Synopsis

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 Read more...

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...


Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data

schema:familyName"Vicente Córdoba"
schema:givenName"José Luis"
schema:name"Vicente Córdoba, José Luis (1941-....)."
schema:name"Resolution of curve and surface singularities in characteristic zero in characteristic zero"

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.