A $\mathbb{Q}$--factorial complete toric variety with Picard number 2 is projective
Abstract
This paper is devoted to settle two still open problems, connected with the existence of ample and nef divisors on a Q-factorial complete toric variety. The first problem is about the existence of ample divisors when the Picard number is 2: we give a positive answer to this question, by studying the secondary fan by means of Z-linear Gale duality. The second problem is about the minimum value of the Picard number allowing the vanishing of the Nef cone: we present a 3-dimensional example showing that this value cannot be greater then 3, which, under the previous result, is also the minimum value guaranteeing the existence of non-projective examples.
Keywords
Cite
@article{arxiv.1504.03850,
title = {A $\mathbb{Q}$--factorial complete toric variety with Picard number 2 is projective},
author = {Michele Rossi and Lea Terracini},
journal= {arXiv preprint arXiv:1504.03850},
year = {2018}
}
Comments
10 pages, 5 figures. Minor changes following the referee's advise: list of notation suppressed, few typos fixed, references updated. Final version to appear in Advances in Geometry