Birational automorphisms of algebraic varieties with a pencil of cubic surfaces
Abstract
Description
It is proved that on a smooth algebraic variety, fibered into cubic surfaces over the projective line and sufficiently ``twisted'' over the base, there is only one pencil of rational surfaces -- that is, this very pencil of cubics. In particular, this variety is non-rational; moreover, it can not be fibered into rational curves. The proof is obtained by means of the method of maximal singularities.
29 pages, latex, to appear in Izvestia
29 pages, latex, to appear in Izvestia