Resolution of curve and surface singularities in characteristic zero
By: by K. Kiyek and J.L. Vicente
Contributors: Vicente Córdoba, José Luis
Series: Algebras and applications -- v. 4
Publisher: Springer
Published: 2011
Place of publication: Dordrecht; London
Language: eng
Number of pages: 485
ISBN-13: 9789048165735
Subjects: Valuation theory; Cohen-Macaulay rings; Singularities (Mathematics); Curves; Algebraic Surfaces
Description: This book covers the beautiful theory of resolutions of surface singularities in characteristic zero. The primary goal is to present in detail, and for the first time in one volume, two proofs for the existence of such resolutions. One construction was introduced by H.W.E. Jung, and another is due to O. Zariski. Jung's approach uses quasi-ordinary singularities and an explicit study of specific surfaces in affine three-space. In particular, a new proof of the Jung-Abhyankar theorem is given via ramification theory. Zariski's method, as presented, involves repeated normalisation and blowing up points. It also uses the uniformization of zero-dimensional valuations of function fields in two variables, for which a complete proof is given. Despite the intention to serve graduate students and researchers of Commutative Algebra and Algebraic Geometry, a basic knowledge on these topics is necessary only. This is obtained by a thorough introduction of the needed algebraic tools in the two appendices.
Notes: Originally published: Dordrecht; London: Kluwer Academic, 2004.

Includes bibliographical references and index.