A characterization of Gorenstein toric Fano $n$-folds with index $n$ and   Fujita's conjecture
  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. 
Shoetsu Ogata and Huai-Liang Zhao
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