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Author Deserti, Julie, author
Title The Cremona group and its subgroups / Julie Deserti
Imprint Providence, Rhode Island : American Mathematical Society, [2021]
2021
book jacket
LOCATION CALL # STATUS OPACMSG BARCODE
 Mathematics Library  QA564 .D47 2021    AVAILABLE    30340200568982
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 173-181) 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 infinite-dimensional hyperbolic space -- Chapter 9. Big subgroups of automorphisms "of positive entropy."
"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."-- 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 infinite-dimensional holomorphy, see 46G20, 58B12} -- Complex spaces with a group of automorphisms -- Complex Lie groups, automorphism groups acting. msc
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