Cremona Groups and the Icosahedron (Chapman & Hall/CRC by Ivan Cheltsov,Constantin Shramov PDF

By Ivan Cheltsov,Constantin Shramov

Cremona teams and the Icosahedron specializes in the Cremona teams of ranks 2 and three and describes the gorgeous appearances of the icosahedral staff A5 in them. The booklet surveys identified evidence approximately surfaces with an motion of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and provides an explanation of its A5-birational rigidity.

The authors explicitly describe many fascinating A5-invariant subvarieties of V5, together with A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular floor of common sort that could be a measure 5 conceal of the diagonal Clebsch cubic floor. additionally they current birational selfmaps of V5 that shuttle with A5-action and use them to figure out the total crew of A5-birational automorphisms. because of this examine, they produce 3 non-conjugate icosahedral subgroups within the Cremona crew of rank three, one in all them coming up from the threefold V5.

This ebook offers up to date instruments for learning birational geometry of higher-dimensional types. particularly, it presents readers with a deep figuring out of the biregular and birational geometry of V5.

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Cremona Groups and the Icosahedron (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) by Ivan Cheltsov,Constantin Shramov

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