Cremona Groups and the Icosahedron Ebook

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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 V5Cremona Groups and the Icosahedron EbookBy Ivan Cheltsov Publisher Chapman and Hall/CRC Print ISBN 9781482251593 1482251590 eText ISBN 9781482251609 1482251604 Edition 1st Copyright year 2015 Format PDF Available from 2318 USD SKU 9781482251609R90 Downloaded copy on your device does not expire

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9781482251593

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 V5Cremona Groups and the Icosahedron EbookBy Ivan Cheltsov Publisher Chapman and Hall/CRC Print ISBN 9781482251593 1482251590 eText ISBN 9781482251609 1482251604 Edition 1st Copyright year 2015 Format PDF Available from 2318 USD SKU 9781482251609R90 Downloaded copy on your device does not expire