A characterization of Gorenstein toric Del Pezzo $n$-folds

TL;DR

This paper characterizes Gorenstein toric Del Pezzo n-folds by providing a condition for lattice n-polytopes to be Gorenstein Fano, avoiding reliance on existing classifications.

Contribution

It offers a new characterization of Gorenstein toric Del Pezzo n-folds and a practical condition for identifying Gorenstein Fano polytopes without using prior classifications.

Findings

Derived a condition for Gorenstein Fano polytopes

Characterized Gorenstein toric Del Pezzo n-folds

Avoided using Batyrev-Juny classification

Abstract

We give a characterizaion of Gorenstein toric Fano $n$-folds with index $n-1$, which is called Gorenstein toric Del Pezzo $n$-folds, among toric varieties. In practice, we obtain a condition for a lattice $n$-polytope to be a Gorenstein Fano polytope. In our proof, we do not use Batyrev-Juny's classification of Gorenstein Fano polytopes.