Generalized Tsen theorem and rationally connected Fano fibrations

Abstract

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.

LaTeX2e, 28 pages, modified proof of 4.2

Cited by in corpus (1)

• Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems