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Cremona Groups and the Icosahedron

Cremona Groups and the Icosahedron

          
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About the Book

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.


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Product Details
  • ISBN-13: 9781482251593
  • Publisher: CRC Press
  • Publisher Imprint: Crc Press
  • Depth: 32
  • Language: English
  • Returnable: Y
  • Spine Width: 30 mm
  • Width: 157 mm
  • ISBN-10: 1482251590
  • Publisher Date: 21 Aug 2015
  • Binding: Hardback
  • Height: 234 mm
  • No of Pages: 528
  • Series Title: Chapman & Hall/CRC Monographs and Research Notes in Mathemat
  • Weight: 883 gr


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