Cremona Groups and the Icosahedron

di Ivan Cheltsov (Autore)

Constantin Shramov (Autore)

Taylor & Francis Inc, 2015

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.

• Autore: Ivan Cheltsov, Constantin Shramov
• Editore: Taylor & Francis Inc
• Collana: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
• Anno: 2015
• Rilegatura: Hardback
• Pagine: 528 p.
• Dimensioni: 234 x 156 mm
• Peso: 861 gr.
• EAN: 9781482251593

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