Cremona Groups and the Icosahedron Hardback
by Ivan Cheltsov, Constantin Shramov
Part of the Chapman & Hall/CRC Monographs and Research Notes in Mathematics series
Hardback
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.
Information
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Out of stock
- Format:Hardback
- Pages:528 pages, 10 Tables, black and white; 36 Illustrations, black and white
- Publisher:Taylor & Francis Inc
- Publication Date:21/08/2015
- Category:
- ISBN:9781482251593
Other Formats
- PDF from £39.68
Information
-
Out of stock
- Format:Hardback
- Pages:528 pages, 10 Tables, black and white; 36 Illustrations, black and white
- Publisher:Taylor & Francis Inc
- Publication Date:21/08/2015
- Category:
- ISBN:9781482251593
