Resolution of curve and surface singularities in characteristic zero
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Author
Contributions
- Vicente Córdoba, José Luis - Contributor
Publication
2011 - Springer, Dordrecht, Netherlands
Language
English
Word Count
121,250 words, Guess
Page Count
485 pages
Identifiers
- Open LibraryOL27085448M
- ISBN-139789048165735
- ISBN-109048165733
- OCLC Control Number751540507
- OCLC Control Numberresolutioncurves00kiye
Classifications
- DDC516.35
- LCCQA564-609
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.
Subjects
Topics
Series Statement
- Algebras and applications -- v. 4
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