A numerical ampleness criterion via Gale duality
Abstract
The main object of the present paper is a numerical criterion determining when a Weil divisor of a --factorial complete toric variety admits a positive multiple Cartier divisor which is either numerically effective (nef) or ample. It is a consequence of --linear interpretation of Gale duality and se\-con\-dary fan as developed in several previous papers of us. As a byproduct we get a computation of the Cartier index of a Weil divisor and a numerical characterization of weak --Fano, --Fano, Gorenstein, weak Fano and Fano toric varieties. Several examples are then given and studied. \keywords{--factorial complete toric variety \and ample divisor \and nef divisor \and -liner Gale duality \and secondary fan \and ampleness criterion \and Cartier index \and -Fano toric variety.
Keywords
Cite
@article{arxiv.1504.07014,
title = {A numerical ampleness criterion via Gale duality},
author = {Michele Rossi and Lea Terracini},
journal= {arXiv preprint arXiv:1504.07014},
year = {2017}
}
Comments
16 pages, 5 figures. v3: minor changes as indicated by the Referees; among them, total renumbering, abstract rewritten, references updated, Remark 2 added to fix a bug in the proof of Thm. 3, results extended to weak Fano toric varieties. Final version to appear in Journal of Applicable Algebra in Engineering, Communication and Computing. arXiv admin note: text overlap with arXiv:1504.06515, arXiv:1507.00493