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portada Open Algebraic Surfaces
Type
Physical Book
Publisher
Author
Collection
CRM Monograph Series
Year
2000
Language
English
Pages
259
Format
Hardcover
ISBN13
9780821805046

Open Algebraic Surfaces

Masayoshi Miyanishi (Author) · American Mathematical Society · Hardcover

Open Algebraic Surfaces - Masayoshi Miyanishi

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Synopsis "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. This book contains an account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine 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"".

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