Birationally rigid varieties with a pencil of Fano double covers. III

摘要

The study of the birational geometry of Fano fibre spaces pi: V --> P-1 with fibre that is a Fano double hypersurface of index 1 is completed. For each family of these varieties either the birational rigidity is proved or non-trivial structures of Fano fibre spaces are explicitly produced. A new linear method of the study of movable systems on Fano fibre spaces V/P-1 is developed.