On the Weights of Root Subgroups of Affine Toric Varieties

Let \(X\) be an affine toric variety and let \(D(X)\) be the set of weights of all root subgroups. It is known that \(D(X)\) together with its embedding into the character group determines \(X\) as a toric variety. In this article we prove that \(X\) is already determined by the abstract set \(D(X)\) together with some additional combinatorial data.