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

Abstract

We complete the study of birational geometry of Fano fiber spaces $\pi :V\to {\mathbb{P}}^1$, 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 $V/{\mathbb{P}}^1$ is developed.

35 pages

References in corpus (6)

• Birational geometry of Fano direct products
• Essentials of the method of maximal singularities
• Birational Geometry of 3-fold Mori Fibre Spaces
• Birationally rigid iterated Fano double covers
• Birational rigidity of a three-dimensional double cone
• Birational properties of pencils of del Pezzo surfaces of degree 1 and 2

Cited by in corpus (5)

• Rationally connected non-Fano type varieties
• Birationally rigid Fano cyclic covers
• Birationally rigid varieties with a pencil of Fano double covers. II
• Birational geometry of Fano double covers
• On the multiplicity of solutions of a system of algebraic equations