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1
Content available remote

Degenerations in the Module Varieties of Generalized Standard Auslander-Reiten Components

100%
Zwara G.
Colloquium Mathematicum
|
1997
|
tom 72
|
nr 2
281-303
2
Content available remote

Degenerations for modules over representation-finite selfinjective algebras

100%
Zwara G.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
91-95
3
Content available remote

An orbit closure for a representation of the Kronecker quiver with bad singularities

100%
Zwara G.
Colloquium Mathematicum
|
2003
|
tom 97
|
nr 1
81-86
EN
We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
4
Content available remote

Immersions of module varieties

100%
Zwara G.
Colloquium Mathematicum
|
1999
|
tom 82
|
nr 2
287-299
EN
We show that a homomorphism of algebras is a categorical epimorphism if and only if all induced morphisms of the associated module varieties are immersions. This enables us to classify all minimal singularities in the subvarieties of modules from homogeneous standard tubes.
5
Content available remote

Schubert varieties and representations of Dynkin quivers

64%
Bobiński G., Zwara G.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 2
285-309
EN
We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that the orbit closures in representation varieties of Dynkin quivers of type 𝔻 are normal and Cohen-Macaulay varieties.
6
Content available remote

Modules and quiver representations whose orbit closures are hypersurfaces

64%
Loc N., Zwara G.
Colloquium Mathematicum
|
2014
|
tom 134
|
nr 1
57-74
EN
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite-dimensional A-modules whose orbit closures are local hypersurfaces. The result is reduced to an analogous characterization for orbit closures of quiver representations obtained in Section 3.
7
Content available remote

On the numbers of discrete indecomposable modules over tame algebras

64%
Skowroński A., Zwara G.
Colloquium Mathematicum
|
1997
|
tom 73
|
nr 1
93-114
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