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Open Algebraic Surfaces
 
Masayoshi Miyanishi Osaka University, Toyonaka, Japan
A co-publication of the AMS and Centre de Recherches Mathématiques
Open Algebraic Surfaces
Hardcover ISBN:  978-0-8218-0504-6
Product Code:  CRMM/12
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3857-9
Product Code:  CRMM/12.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-0504-6
eBook: ISBN:  978-1-4704-3857-9
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
Open Algebraic Surfaces
Click above image for expanded view
Open Algebraic Surfaces
Masayoshi Miyanishi Osaka University, Toyonaka, Japan
A co-publication of the AMS and Centre de Recherches Mathématiques
Hardcover ISBN:  978-0-8218-0504-6
Product Code:  CRMM/12
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3857-9
Product Code:  CRMM/12.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-0504-6
eBook ISBN:  978-1-4704-3857-9
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 Details
     
     
    CRM Monograph Series
    Volume: 122000; 259 pp
    MSC: 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 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.

    Titles in this series are co-published with the Centre de recherches mathématiques.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 122000; 259 pp
MSC: 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 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.

Titles in this series are co-published with the Centre de recherches mathématiques.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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