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Resolution of singularities of embedded algebraic surfaces.

Author: Shreeram Shankar Abhyankar
Publisher: New York : Academic Press, 1966.
Series: Pure and applied mathematics (Academic Press), 24.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Abhyankar, Shreeram Shankar.
Resolution of singularities of embedded algebraic surfaces.
New York : Academic Press, 1966
(DLC) 66026258
(OCoLC)525591
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Shreeram Shankar Abhyankar
ISBN: 9780080873367 0080873367 0120419564 9780120419562
OCLC Number: 316566914
Description: 1 online resource (ix, 291 pages).
Contents: Front Cover; Resolution of Singularities of Embedded Algebraic Surfaces; Copyright Page; Preface; Contents; Chapter 0. Introduction; Chapter 1. Local Theory; Chapter 2. Global Theory; Chapter 3. Some Cases of Three-Dimensional Birational Resolution; Index of Notation; Index of Definitions.
Series Title: Pure and applied mathematics (Academic Press), 24.

Abstract:

This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. The book can be used for a second year graduate course. The reference list has been updated.

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