**CRM Monograph Series**

Volume: 12;
2000;
259 pp;
Hardcover

MSC: Primary 14;

Print ISBN: 978-0-8218-0504-6

Product Code: CRMM/12

List Price: $72.00

Individual Member Price: $57.60

**Electronic ISBN: 978-1-4704-3857-9
Product Code: CRMM/12.E**

List Price: $72.00

Individual Member Price: $57.60

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# Open Algebraic Surfaces

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*Masayoshi Miyanishi*

A co-publication of the AMS and Centre de Recherches Mathématiques

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,

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.

#### Reviews & Endorsements

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

-- CMS Notes