Curves disjoint from a nef divisor
Algebraic Geometry
2014-10-17 v1
Abstract
On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing a nef line bundle on a threefold which is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.
Cite
@article{arxiv.1410.4467,
title = {Curves disjoint from a nef divisor},
author = {John Lesieutre and John Christian Ottem},
journal= {arXiv preprint arXiv:1410.4467},
year = {2014}
}
Comments
7 pages; comments welcome!