Hardcover ISBN:  9780821805046 
Product Code:  CRMM/12 
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eBook ISBN:  9781470438579 
Product Code:  CRMM/12.E 
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AMS Member Price:  $88.00 
Hardcover ISBN:  9780821805046 
eBook: ISBN:  9781470438579 
Product Code:  CRMM/12.B 
List Price:  $225.00 $170.00 
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AMS Member Price:  $180.00 $136.00 
Hardcover ISBN:  9780821805046 
Product Code:  CRMM/12 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470438579 
Product Code:  CRMM/12.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 
Hardcover ISBN:  9780821805046 
eBook ISBN:  9781470438579 
Product Code:  CRMM/12.B 
List Price:  $225.00 $170.00 
MAA Member Price:  $202.50 $153.00 
AMS Member Price:  $180.00 $136.00 

Book DetailsCRM Monograph SeriesVolume: 12; 2000; 259 ppMSC: Primary 14
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 EnriquesKodaira 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 EnriquesKodaira 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.
Titles in this series are copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and research mathematicians interested in algebraic geometry and polynomial rings.

Table of Contents

Chapters

Complete algebraic surfaces

Open algebraic surfaces

Affine algebraic surfaces


Reviews

An indispensible reference work for experts in the field ... will do a lot to open this exciting area of mathematics to newcomers.
CMS Notes


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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 EnriquesKodaira 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 EnriquesKodaira 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.
Titles in this series are copublished with the Centre de recherches mathématiques.
Graduate students and research mathematicians interested in algebraic geometry and polynomial rings.

Chapters

Complete algebraic surfaces

Open algebraic surfaces

Affine algebraic surfaces

An indispensible reference work for experts in the field ... will do a lot to open this exciting area of mathematics to newcomers.
CMS Notes