On the resolution of singularities in affine toric 3-varieties (Q1329587)

Let \(X_{\Sigma (\sigma)} = \text{Spec} \mathbb{C} [\check \sigma \cap \mathbb{Z}^ 3]\) be an affine toric variety given by the monoid algebra \(\mathbb{C} [\check \sigma \cap \mathbb{Z}^ 3]\), \(\check \sigma\) the negative dual cone of a lattice cone \(\sigma \subset \mathbb{R}^ 3\), \(\Sigma (\sigma)\) the fan consisting of the faces of \(\sigma\). The authors classify all pairs \(X_{\Sigma'}\), \(X_{\Sigma (\sigma)}\) which occur in minimal models of equivariant resolutions \(\Phi : X_{\Sigma'} \to X_{\Sigma (\sigma)}\), such that \(X_{\Sigma (\sigma)}\) has only quotient singularities and the regular toric variety \(X_{\Sigma'}\) has Picard number at most 3. All the possible generators \((a_ 1, a_ 2, a_ 3)\) are given and all the corresponding fans \(\Sigma'\) are drawn.