ENGLISH

The Cremona Group and Its Subgroups

By Julie Déserti

Book information

Publisher
American Mathematical Soc.
Year
2021
ISBN
9781470460129, 1470460122
Google Books ID
BnwqEAAAQBAJ
Language
english
Format
PDF
Filesize
2 MB (2094690 bytes)
Series
Mathematical Surveys and Monographs, Vol. 252
Edition
1
Pages
187\202
Time added
2023-12-30 02:29:36

Description

The goal of this book is to present a portrait of the n 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.

Similar books