Central singularities of quantum spaces (Q1908466)

Let \(A\) be a positively graded connected affine \(\mathbb{C}\)-algebra generated in degree one. Let \(R\) be a central graded subalgebra and assume that \(A\) is a finite module over \(R\). Then \(A\) gives rise to a coherent sheaf \({\mathcal A}\) of algebras over \(Y = \text{Proj} R\); the center \({\mathcal Z}\) of \({\mathcal A}\) (a sheaf of commutative algebras) plays a rôle in the study of Sklyanin algebras at points of finite order. Assume that \(\text{injdim} (A) < \infty\). It is shown in the present paper that the commutative scheme \(\text{Spec} {\mathcal Z}\) has singularities unless the ramification locus of \({\mathcal A}\) is pure of codimension 1. If \(\text{gldim} (A) < \infty\), then the codimension \(\geq 2\) parts of the ramification locus of \({\mathcal A}\) and the singular locus of \(\text{Spec} {\mathcal Z}\) coincide.