Cremona Groups and the Icosahedron Contributor(s): Cheltsov, Ivan (Author), Shramov, Constantin (Author) |
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ISBN: 1482251590 ISBN-13: 9781482251593 Publisher: CRC Press OUR PRICE: $190.00 Product Type: Hardcover - Other Formats Published: August 2015 |
Additional Information |
BISAC Categories: - Mathematics | Algebra - General - Mathematics | Geometry - Algebraic - Mathematics | Number Theory |
Dewey: 516.35 |
LCCN: 2015027401 |
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathemat |
Physical Information: 1.2" H x 6.2" W x 9.2" (1.95 lbs) 528 pages |
Descriptions, Reviews, Etc. |
Publisher 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. |