A characterization of Gorenstein toric Fano $n$-folds with index $n$ and Fujita's conjecture

Abstract

We give a characterization of Gorenstein toric Fano varieties of dimension $n$ with index $n$ among toric varieties. As an application, we give a strong version of Fujita's freeness conjecture and also give a simple proof of Fujita's very ampleness conjecture on Gorenstein toric varieties.