On minimal disjoint degenerations for preprojective representations of quivers

Bongartz, Klaus; Fritzsche, Thomas

doi:10.1090/S0025-5718-03-01503-5

On minimal disjoint degenerations for preprojective representations of quivers
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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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