Grzegorz Bobiński

Classification of discrete derived categories

The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.

Normality of orbit closures for Dynkin quivers¶of type ?n

Abstract: It is known that the orbit closures for the representations of the equioriented Dynkin quivers ?n are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers ?n with arbitrary orientation.

Geometry of Periodic Modules over Tame Concealed and Tubular Algebras

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.

Geometry of regular modules over canonical algebras

We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules normality is equivalent to irreducibility.

On moduli spaces for quasitilted algebras

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.

Domestic Algebras with Many Nonperiodic Auslander–Reiten Components

Abstract We exhibit a wide class of domestic finite dimensional algebras over an algebraically closed field whose Auslander–Reiten quivers admit infinitely many connected components of type ℤ𝔻∞ (respectively, of types ℤ𝔻∞ and ℤ ). The algebras are suitable iterated one-point extensions of hereditary algebras of Euclidean type 𝔸˜ n .

On a family of vector space categories

In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.

Domestic iterated one-point extensions of algebras by two-ray modules

In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.

Canonical Tilting Modules Over Shod Algebras are Regular in Codimension One

We show that for a class of modules over shod algebras, including the canonical tilting modules, the closures of the corresponding orbits in module varieties are regular in codimension one.

Normal Forms of Modules over Admissible Algebras with Formal Two-ray Modules

AbstractThe aim of the paper is to classify the indecomposable modules and describe the Auslander- Reiten sequences for the admissible algebras with formal two-ray modules.