Birational geometry of varieties fibred into complete intersections of codimension two

Abstract

In this paper we prove the birational superrigidity of Fano–Mori fibre spaces all of whose fibres are complete intersections of type in the projective space satisfying certain conditions of general position, under the assumption that the fibration is sufficiently twisted over the base (in particular, under the assumption that the -condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition also bounds the dimension of the base by a constant depending only on the dimension of the fibre (this constant grows like as ). The fibres and the variety may have quadratic and bi-quadratic singularities whose rank is bounded below.