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 attractive appearances of the icosahedral team 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 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 common style that may 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 team of A5-birational automorphisms. due to this examine, they produce 3 non-conjugate icosahedral subgroups within the Cremona workforce of rank three, one in every of them bobbing up from the threefold V5.
This booklet offers updated instruments for learning birational geometry of higher-dimensional types. particularly, it presents readers with a deep knowing of the biregular and birational geometry of V5.