| Descript |
xii, 187 pages : illustrations ; 26 cm |
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text txt rdacontent |
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unmediated n rdamedia |
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volume nc rdacarrier |
| Series |
Mathematical surveys and monographs ; volume 252 |
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Mathematical surveys and monographs ; volume 252
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| Note |
Includes bibliographical references (pages 173-181) and indexes |
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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." |
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"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
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Geometry, Algebraic. fast (OCoLC)fst00940902
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Algebraic geometry -- Birational geometry -- Birational automorphisms, Cremona group and generalizations. msc
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Algebraic geometry -- Birational geometry -- Rational and birational maps. msc
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Group theory and generalizations -- Research exposition (monographs, survey articles). msc
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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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