Geometry of Periodic Modules over Tame Concealed and Tubular Algebras

Abstract

Listen

Translate article

Let A be a tame concealed or tubular algebra and d the dimension-vector of a periodic module with respect to the action of the Auslander–Reiten translation. We prove that the affine variety modA(d) of all A-modules of dimension-vector d is a normal complete intersection. Moreover, we show that a module M in modA(d) is nonsingular if and only if ExtA2(M,M)=0.