Generalized Tsen theorem and rationally connected Fano fibrations
- Author(s): Campana, Frederic;
- Peternell, Thomas;
- Pukhlikov, Aleksandr
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/0110017.pdf
We prove that a fibration X \to \Bbb P_1, the general fiber of which is a smooth Fano threefold, is rationally connected. The proof is based on a generalization of Tsen's classical theorem: a fibration X/C over a curve the general fiber of which is a Fano complete intersection in a product of weighted projective spaces has a section.