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.
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