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


We complete the study of birational geometry of Fano fiber spaces π: V → P 1 , the fiber of which is a Fano double hypersurface of index 1. For each family of these varieties we either prove birational rigidity or produce explicitly non-trivial structures of Fano fiber spaces. A new linear method of studying movable systems on Fano fiber spaces V /P 1 is… (More)