Generalized Tsen theorem and rationally connected Fano fibrations
Frederic Campana, Thomas Peternell, Aleksandr Pukhlikov
Abstract
We prove that a fibration X P1, 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.
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