On minimal disjoint degenerations for preprojective representations of quivers |
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Authors: | Klaus Bongartz Thomas Fritzsche |
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Institution: | FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany ; FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany |
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Abstract: | We derive a root test for degenerations as described in the title. In the case of Dynkin quivers this leads to a conceptual proof of the fact that the codimension of a minimal disjoint degeneration is always one. For Euclidean quivers, it enables us to show a periodic behaviour. This reduces the classification of all these degenerations to a finite problem that we have solved with the aid of a computer. It turns out that the codimensions are bounded by two. Somewhat surprisingly, the regular and preinjective modules play an essential role in our proofs. |
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