By Ivan Cheltsov,Constantin Shramov
Cremona teams and the Icosahedron specializes in the Cremona teams of ranks 2 and three and describes the attractive appearances of the icosahedral team A5 in them. The e-book surveys identified proof approximately surfaces with an motion of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and offers 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 normal sort that could be a measure 5 conceal of the diagonal Clebsch cubic floor. additionally they current birational selfmaps of V5 that go back and forth with A5-action and use them to figure out the complete crew of A5-birational automorphisms. because of this examine, they produce 3 non-conjugate icosahedral subgroups within the Cremona workforce of rank three, considered one of them coming up from the threefold V5.
This booklet provides up to date instruments for learning birational geometry of higher-dimensional types. specifically, it offers readers with a deep realizing 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