Smooth rationally connected threefolds contain all smooth curves
Algebraic Geometry
2010-02-05 v2
Abstract
We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We give some details about the toric case.
Cite
@article{arxiv.0710.3290,
title = {Smooth rationally connected threefolds contain all smooth curves},
author = {G. K. Sankaran},
journal= {arXiv preprint arXiv:0710.3290},
year = {2010}
}
Comments
Version 1 was called "Any smooth toric threefold contains all curves". This version is completely rewritten and proves a much stronger result, following suggestions of Janos Kollar