English

Generalized Tsen theorem and rationally connected Fano fibrations

Algebraic Geometry 2015-06-26 v2

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.

Keywords

Cite

@article{arxiv.math/0110017,
  title  = {Generalized Tsen theorem and rationally connected Fano fibrations},
  author = {Frederic Campana and Thomas Peternell and Aleksandr Pukhlikov},
  journal= {arXiv preprint arXiv:math/0110017},
  year   = {2015}
}

Comments

LaTeX2e, 28 pages, modified proof of 4.2

R2 v1 2026-07-22T16:40:39.326Z