Cremona Groups and the Icosahedron (Hardcover)

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.

General

Imprint:	Apple Academic Press Inc.
Country of origin:	Canada
Series:	Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Release date:	August 2015
First published:	2015
Authors:	Ivan Cheltsov • Constantin Shramov
Dimensions:	234 x 156 x 36mm (L x W x T)
Format:	Hardcover
Pages:	528
ISBN-13:	978-1-4822-5159-3
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	1-4822-5159-0
Barcode:	9781482251593

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