Cremona Groups and the Icosahedron

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 s...