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Springer Monographs in Mathematics Ser.: Resolution of Singularities of Embedded Algebraic Surfaces by Shreeram Shankar Abhyankar (1998, Hardcover)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540637192
ISBN-139783540637196
eBay Product ID (ePID)544365
Product Key Features
Number of PagesXii, 312 Pages
Publication NameResolution of Singularities of Embedded Algebraic Surfaces
LanguageEnglish
SubjectAlgebra / General, Number Theory, Geometry / Algebraic
Publication Year1998
TypeTextbook
AuthorShreeram Shankar Abhyankar
Subject AreaMathematics
SeriesSpringer Monographs in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight49.4 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN98-009728
Dewey Edition21
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.5
Table Of Content0 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.
Edition DescriptionEnlarged edition,Revised edition
SynopsisBesides the description of the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic, this new edition provides a self-contained introduction to birational algebraic geometry, based only on commutative algebra. It also gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996., The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. A cusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives abirational transformation of a variety. Singularities of a variety may be resolved by birational transformations.
LC Classification NumberQA564-609
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