Cremona Groups and the Icosahedron

Focusing on Cremona groups and their icosahedral subgroups, this book provides an ideal introduction to birational geometry for researchers and graduate students. The first results of the Cremona group of rank two go back to the time of Appollonius. But the map of the Cremona group is not often defined at some points, making it very hard to study. This book introduces the Cremona group of rank three, which is very large and impossible to handle directly. The book helps readers develop new methods for the study of finite subgroups of Cremona groups of high rank or Cremona groups of rank three.

Ivan Cheltsov is a professor in the School of Mathematics at the University of Edinburgh. Dr. Cheltsov’s research focuses on birational geometry and its connections with algebra, geometry, and topology, including del Pezzo surfaces, Fano threefolds, and Cremona groups.

Constantin Shramov is a researcher at Steklov Mathematical Institute and Higher School of Economics in Moscow. Dr. Shramov’s research interests include birational geometry, Fano varieties, minimal model program, log-canonical thresholds, Kahler–Einstein metrics, Cremona groups, and birational rigidity.