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1. Preliminaries -- 2. Icosahedral group -- 3. Quintic del Pezzo threefold -- 4. Invariant subvarieties -- 5. Singularities of linear systems.
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 Pe…
"We prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid."--Publisher website.
