Resolution of Singularities of Embedded Algebraic Surfaces

Shreeram Shankar Abhyankar

312 pages, parution le 01/06/1998

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Résumé

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.

Contents

Preface to the Second Edition
Preface to the First Edition
Introduction 1

Ch. 1 Local Theory

1 Terminology and preliminaries 7
2 Resolvers and principalizers 45
3 Dominant character of a normal sequence 61
4 Unramified local extensions 108
5 Main results 148

Ch. 2 Global Theory

6 Terminology and preliminaries 155
7 Global resolvers 192
8 Global principalizers 223
9 Main results 233

Ch. 3 Some Cases of Three-Dimensional Birational Resolution

10 Uniformization of points of small multiplicity 238
11 Three-dimensional birational resolution over a ground field of characteristic zero 261
12 Existence of projective models having only points of small multiplicity 262
13 Three-dimensional birational resolution over an algebraically closed ground field of characteristic 2, 3, 5 283

Appendix on Analytic Desingularization in Characteristic Zero 285
Bibliography 301
Additional Bibliography 303
Index of Notation 305
Index of Definitions 307
List of Corrections

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Shreeram Shankar Abhyankar
Parution	01/06/1998
Nb. de pages	312
Format	16 x 24
Couverture	Relié
Poids	598g
Intérieur	Noir et Blanc
EAN13	9783540637196