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

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

2005-10-08

arxiv.org/abs/math/0510168v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

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

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