Descript 
xii, 187 pages : illustrations ; 26 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
Series 
Mathematical surveys and monographs ; volume 252 

Mathematical surveys and monographs ; volume 252

Note 
Includes bibliographical references (pages 173181) and indexes 

Chapter 1. Introduction  Chapter 2. An isometric action of the Cremona group on an infinite dimensional hyperbolic space  Chapter 3. Algebraic subgroups of the Cremona group  Chapter 4. Generators and relations of the Cremona group == Chapter 5. Algebraic properties of the Cremona group  Chapter 6. Finite subgroups of the Cremona group  Chapter 7. Uncountable subgroups of the Cremona group  Chapter 8. Consequences of the action of the Cremona group on an infinitedimensional hyperbolic space  Chapter 9. Big subgroups of automorphisms "of positive entropy." 

"The goal of this book is to present a portrait of the ndimensional Cremona group with an emphasis on the 2dimensional 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." Provided by publisher 
Subject 
Geometry, Algebraic


Geometry, Algebraic. fast (OCoLC)fst00940902


Algebraic geometry  Birational geometry  Birational automorphisms, Cremona group and generalizations. msc


Algebraic geometry  Birational geometry  Rational and birational maps. msc


Group theory and generalizations  Research exposition (monographs, survey articles). msc


Several complex variables and analytic spaces {For infinitedimensional holomorphy, see 46G20, 58B12}  Complex spaces with a group of automorphisms  Complex Lie groups, automorphism groups acting. msc

