The Cremona group and its subgroups
著者
書誌事項
The Cremona group and its subgroups
（Mathematical surveys and monographs, v. 252）
American Mathematical Society, c2021
- : pbk
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注記
Includes bibliographical references (p. 173-181) and indexes
内容説明・目次
内容説明
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.
目次
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''
Bibliography
Index
Index notations
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