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Resolution of Singularities of Embedded Algebraic Surfaces

Resolution of Singularities of Embedded Algebraic Surfaces
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Field name Details
Dewey Class 516.35
Title Resolution of Singularities of Embedded Algebraic Surfaces ([EBook] /) / by Shreeram S. Abhyankar.
Author Abhyankar, Shreeram Shankar
Other name(s) SpringerLink (Online service)
Edition statement Second, Enlarged Edition.
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg : , 1998.
Physical Details XII, 312 p. : online resource.
Series Springer monographs in mathematics 1439-7382
ISBN 9783662035801
Summary Note 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. It can can be used for a second year graduate course. The reference list has been updated.:
Contents note 0 Introduction -- 1. Local Theory -- 1 Terminology and preliminaries -- 2 Resolvers and principalizers -- 3 Dominant character of a normal sequence -- 4 Unramified local extensions -- 5 Main results -- 2. Global Theory -- 6 Terminology and preliminaries -- 7 Global resolvers -- 8 Global principalizers -- 9 Main results -- 3. Some Cases of Three-Dimensional Birational Resolution -- 10 Uniformization of points of small multiplicity -- 11 Three-dimensional birational resolution over a ground field of characteristic zero -- 12 Existence of projective models having only points of small multiplicity -- 13 Three-dimensional birational resolution over an algebraically closed ground field of charateristic ? 2, 3, 5 -- Appendix on Analytic Desingularization in Characteristic Zero -- Additional Bibliography -- Index of Notation -- Index of Definitions -- List of Corrections.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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