Cremona Groups and the Icosahedron, Hardback Book

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

  • Format: Hardback
  • Pages: 527 pages, No Color; 10 Tables, black and white; 36 Illustrations, black and white
  • Publisher: Apple Academic Press Inc.
  • Publication Date:
  • Category: Algebraic geometry
  • ISBN: 9781482251593

£75.99

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