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Birational automorphisms of algebraic varieties with a pencil of cubic surfaces

Aleksandr V. Pukhlikov
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Abstract

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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Aleksandr V. Pukhlikov. 1996-11-08. Birational automorphisms of algebraic varieties with a pencil of cubic surfaces. https://arxiv.org/abs/alg-geom/9611009

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