The main object of the present paper is a numerical criterion determining when a Weil divisor of a QQ –factorial complete toric variety admits a positive multiple Cartier divisor which is either numerically effective (nef) or ample. It is a consequence of ZZ –linear interpretation of Gale duality and secondary 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 QQ –Fano, QQ –Fano, Gorenstein, weak Fano and Fano toric varieties. Several examples are then given and studied.

A numerical ampleness criterion via Gale duality

ROSSI, Michele;TERRACINI, Lea
2017-01-01

Abstract

The main object of the present paper is a numerical criterion determining when a Weil divisor of a QQ –factorial complete toric variety admits a positive multiple Cartier divisor which is either numerically effective (nef) or ample. It is a consequence of ZZ –linear interpretation of Gale duality and secondary 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 QQ –Fano, QQ –Fano, Gorenstein, weak Fano and Fano toric varieties. Several examples are then given and studied.
2017
28
351
368
http://link.springer.com/article/10.1007%2Fs00200-016-0308-5
QQ –factorial complete toric variety, Ample divisor, Nef divisor, ZZ-liner Gale duality, Secondary fan, Ampleness criterion, Cartier index, QQ-Fano toric variety
Rossi, Michele; Terracini, Lea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1616962
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