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

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 crew A5 in them. The ebook surveys recognized evidence approximately surfaces with an motion of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and offers an evidence 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 normal variety that may be a measure 5 disguise of the diagonal Clebsch cubic floor. in addition they current birational selfmaps of V5 that go back and forth with A5-action and use them to figure out the entire team of A5-birational automorphisms. due to this learn, they produce 3 non-conjugate icosahedral subgroups within the Cremona workforce of rank three, one among 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 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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