Cremona groups and the icosahedron
Author(s)
Bibliographic Information
Cremona groups and the icosahedron
（Monographs and research notes in mathematics）（A Chapman & Hall book）
CRC Press, Taylor & Francis Group, c2016
- : hardback
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackCHE||76||1200033912177
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Note
Includes bibliographical references (p. 485-494) and index
Description and Table of Contents
Description
Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity.
The authors explicitly describe many interesting A5-invariant subvarieties of V5, including A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular surface of general type that is a degree five cover of the diagonal Clebsch cubic surface. They also present two birational selfmaps of V5 that commute with A5-action and use them to determine the whole group of A5-birational automorphisms. As a result of this study, they produce three non-conjugate icosahedral subgroups in the Cremona group of rank 3, one of them arising from the threefold V5.
This book presents up-to-date tools for studying birational geometry of higher-dimensional varieties. In particular, it provides readers with a deep understanding of the biregular and birational geometry of V5.
Table of Contents
Preliminaries. Icosahedral Group. Quintic del Pezzo Threefold. Invariant Subvarieties. Singularities of Linear Systems.
by "Nielsen BookData"