On minimal disjoint degenerations of modules over tame path algebras

TL;DR

This paper investigates minimal disjoint degenerations of modules over tame path algebras, establishing bounds on their codimensions and linking these bounds to the classification of quivers as Dynkin, Euclidean, or wild.

Contribution

It proves that codimensions of minimal disjoint degenerations are bounded by 2 and connects these bounds to quiver classifications, providing a finite classification approach.

Findings

Codimensions are bounded by 2 for tame quivers.

Quiver type (Dynkin, Euclidean, wild) correlates with codimension bounds.

Complete classification of minimal disjoint degenerations is computationally feasible.

Abstract

We study minimal disjoint degenerations for representations of tame quivers. In particular, we prove that their codimensions are bounded by 2. Therefore a quiver is Dynkin resp. Euclidean resp. wild iff the codimensions are 1 resp. bounded by 2 resp. unbounded. We explain also that for tame quivers the complete classification of all minimal disjoint degenerations is a finite problem that can be solved with the help of a computer.