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

By Ivan Cheltsov,Constantin Shramov

Cremona teams and the Icosahedron makes a speciality of the Cremona teams of ranks 2 and three and describes the gorgeous appearances of the icosahedral staff A5 in them. The ebook surveys identified proof 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 attention-grabbing A5-invariant subvarieties of V5, together with A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular floor of common variety that could be a measure 5 disguise of the diagonal Clebsch cubic floor. additionally they current birational selfmaps of V5 that travel with A5-action and use them to figure out the total team of A5-birational automorphisms. because of this examine, they produce 3 non-conjugate icosahedral subgroups within the Cremona team of rank three, one in every of them bobbing up from the threefold V5.

This publication provides updated instruments for learning birational geometry of higher-dimensional forms. specifically, it presents readers with a deep knowing of the biregular and birational geometry of V5.

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