English

Extending rationally connected fibrations from ample subvarieties

Algebraic Geometry 2020-11-23 v1

Abstract

Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply this result in the context of Fano fibrations and prove a classification theorem for projective bundle and quadric fibration structures on ample subvarieties.

Keywords

Cite

@article{arxiv.2011.10567,
  title  = {Extending rationally connected fibrations from ample subvarieties},
  author = {Tommaso de Fernex and Chung Ching Lau},
  journal= {arXiv preprint arXiv:2011.10567},
  year   = {2020}
}

Comments

13 pages. formerly last two sections of arXiv:1911.10385

R2 v1 2026-06-23T20:24:14.091Z