Geometry of periodic modules over tame concealed and tubular algebras (Q1610227)

Let \(k\) be an algebraically closed field, let \(A\) be a tame concealed or tubular finite-dimensional \(k\)-algebra, and let \(\mathbf d\) be the dimension-vector of a periodic module over \(A\) with respect to the action of the Auslander-Reiten translation [\textit{C. M. Ringel}, Tame algebras and integral quadratic forms. (Lect. Notes Math. 1099) (1984; Zbl 0546.16013)]. It is proved that the affine variety \(\text{mod}_A({\mathbf d})\) of all \(A\)-modules \(M\) of dimension-vector \(\mathbf d\) is a reduced irreducible normal complete intersection. Moreover, a point \(\{M\}\in\text{mod}_A({\mathbf d})\) is nonsingular if and only if \(\text{Ext}^2_A(M,M)=0\).