Birational automorphisms of algebraic varieties with a pencil of cubic surfaces

Details Birational automorphisms of algebraic varieties with a pencil of cubic surfaces Birational automorphisms of algebraic varieties with a pencil of cubic surfaces

1996-11-08

arxiv.org/abs/alg-geom/9611009v1

Mathematics

Algebraic Geometry

29 pages, latex, to appear in Izvestia

Scientific paper

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.

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