By Ivan Cheltsov, Constantin Shramov

ISBN-10: 1482251604

ISBN-13: 9781482251609

ISBN-10: 4134154154

ISBN-13: 9784134154150

**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 A_{5} in them. The ebook surveys identified proof approximately surfaces with an motion of A_{5}, explores A_{5}-equivariant geometry of the quintic del Pezzo threefold *V*_{5}, and offers an evidence of its A_{5}-birational rigidity.

The authors explicitly describe many fascinating A_{5}-invariant subvarieties of *V*_{5}, together with A_{5}-orbits, low-degree curves, invariant anticanonical *K*3 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 *V*_{5} that shuttle with A_{5}-action and use them to figure out the total team of A_{5}-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 *V*_{5}.

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 *V*_{5}.