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

TL;DR

This paper characterizes Gorenstein toric Fano n-folds with index n and applies this to prove a strong version of Fujita's freeness conjecture and a simple proof of Fujita's very ampleness conjecture for Gorenstein toric varieties.

Contribution

It provides a characterization of Gorenstein toric Fano varieties with index n and advances Fujita's conjectures in the toric setting.

Findings

Characterization of Gorenstein toric Fano n-folds with index n.

A strong version of Fujita's freeness conjecture.

A simple proof of Fujita's very ampleness conjecture for Gorenstein toric varieties.

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.