Geometry of modules over tame quasi-tilted algebras

Abstract

We prove that if a quasi-tilted algebra is tame, then the associated moduli spaces are products of projective spaces. Together with an earlier result of Chindris this gives a geometric characterization of the tame quasi-tilted algebras. In proof we use knowledge of the representation theory of the tame quasi-tilted algebras and a construction of semi-invariants as determinants.

On Regularity in Codimension One of Irreducible Components of Module Varieties

“…The results of [8] imply that both factors are normal, hence regular in codimension one, and the claim follows for this component.…”

“…This strategy has been successfully applied in [5,8,9,11]. In particular, the main results of [8,9] imply that if d is the dimension vector of an indecomposable module over a tame quasi-tilted algebra Λ, then mod Λ (d) has at most two irreducible components.…”

“…Up to duality, we may assume that X ∈ X . A discussion of this case presented in [8,Section 5] shows that under this assumption one of the irreducible components of mod …”

Geometry of regular modules over canonical algebras

“…Our first theorem generalizes to regular modules over arbitrary canonical algebra a result obtained for indecomposable modules over tame canonical algebra in [2]. …”

On the Geometry of Orbit Closures for Representation-Infinite Algebras

“…Let h be the unique isotropic Schur root of A. The module variety mod(A, h) is irreducible by Corollary 3 in [2], and let us denote its cone of effective weights by Eff(A, h). We know from Lemma 3.2 that there exists a module M ∈ mod(A, h) which is θ h -stable.…”