Open Algebraic Surfaces

Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities.This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic background in algebraic geometry. This volume is a continuation of the work presented in the author's previous publication, "Algebraic Geometry, Volume 136" in the AMS series, "Translations of Mathematical Monographs".

ISBN 0821805045   Pages 259 ISBN13 9780821805046 (What's this?)   Volumes 001 Publisher American Mathematical Society   Weight (grammes) 686 Imprint American Mathematical Society   Published in Providence Format Hardback   Series title CRM Monograph Series Publication date 15 Nov 2000   Height (mm) 230 Library of Congress QA571. M58   Width (mm) 178 DEWEY 516.35   Academic level Professional / Scholarly DEWEY edition DC21

		Preface
Ch. 1		Complete Algebraic Surfaces		1
1		Fundamental Theorems on Algebraic Surfaces		1
2		Ruled Surfaces		10
3		Elliptic or Quasi-Elliptic Fibrations		23
4		Enriques-Kodaira Classification of Algebraic Surfaces		41
5		Normal Singular Surfaces		51
Ch. 2		Open Algebraic Surfaces		59
1		Kodaira Dimensions		59
2		Algebraic Surfaces with Logarithmic Kodaira Dimension -[infinity]		72
3		Theory of Peeling		86
4		Log Projective Surfaces and Minimal Models		117
5		Log del Pezzo Surfaces of Rank 1		142
6		Structure Theorems for Open Algebraic Surfaces with Kodaira Dimension 0 or 1		173
Ch. 3		Affine Algebraic Surfaces		193
1		Fibrations		193
2		Algebraic Characterizations of the Affine Plane		205
3		Theorem of Abhyankar-Moh-Suzuki and Theorem of Lin-Zaidenberg		220
4		Homology Planes		228
		Bibliography		253
		Index		257

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