Resolution of singularities of embedded algebraic surfaces.

By:

Abhyankar, Shreeram Shankar

Contributor(s):

ScienceDirect eBooks

Series: Pure and applied mathematics (Academic Press) ; 24.1966Description: 1 online resource (ix, 291 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9780080873367
0080873367
0120419564
9780120419562

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version:: Resolution of singularities of embedded algebraic surfaces.LOC classification:

QA3 .P8 vol. 24eb

Online resources:

Click here to access online

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.

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 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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eBooks

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Includes bibliographical references (pages 285-286).

Print version record.

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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