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The Cremona Group and Its Subgroups
 
Julie Déserti Université Côte d’Azur, Nice, France
The Cremona Group and Its Subgroups
Softcover ISBN:  978-1-4704-6012-9
Product Code:  SURV/252
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6452-3
Product Code:  SURV/252.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6012-9
eBook: ISBN:  978-1-4704-6452-3
Product Code:  SURV/252.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
The Cremona Group and Its Subgroups
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The Cremona Group and Its Subgroups
Julie Déserti Université Côte d’Azur, Nice, France
Softcover ISBN:  978-1-4704-6012-9
Product Code:  SURV/252
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6452-3
Product Code:  SURV/252.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6012-9
eBook ISBN:  978-1-4704-6452-3
Product Code:  SURV/252.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2522021; 187 pp
    MSC: Primary 14; 20; 32

    The goal of this book is to present a portrait of the \(n\)-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts.

    This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations.

    The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions.

    This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.

    Readership

    Graduate students and researchers interested in birational automorphisms and complex algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • An isometric action of the Cremona group on an infinite dimensional hyperbolic space
    • Algebraic subgroups of the Cremona group
    • Generators and relations of the Cremona group
    • Algebraic properties of the Cremona group
    • Finite subgroups of the Cremona group
    • Uncountable subgroups of the Cremona group
    • Consequences of the action of the Cremona group of an infinite dimensional hyperbolic space
    • Big subgroups of autmorphisms “of positive entropy”
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2522021; 187 pp
MSC: Primary 14; 20; 32

The goal of this book is to present a portrait of the \(n\)-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts.

This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations.

The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions.

This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.

Readership

Graduate students and researchers interested in birational automorphisms and complex algebraic geometry.

  • Chapters
  • Introduction
  • An isometric action of the Cremona group on an infinite dimensional hyperbolic space
  • Algebraic subgroups of the Cremona group
  • Generators and relations of the Cremona group
  • Algebraic properties of the Cremona group
  • Finite subgroups of the Cremona group
  • Uncountable subgroups of the Cremona group
  • Consequences of the action of the Cremona group of an infinite dimensional hyperbolic space
  • Big subgroups of autmorphisms “of positive entropy”
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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