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. --factorial complete toric variety ample divisor nef divisor -liner Gale duality secondary fan ampleness criterion Cartier index -Fano toric variety.
0