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On minimal disjoint degenerations for preprojective representations of quivers
Author(s):
Klaus
Bongartz;
Thomas
Fritzsche.
Journal:
Math. Comp.
72
(2003),
2013-2042.
MSC (2000):
Primary 16G20, 14L30
Posted:
February 3, 2003
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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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Additional Information:
Klaus
Bongartz
Affiliation:
FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
Email:
Klaus.Bongartz@math.uni-wuppertal.de
Thomas
Fritzsche
Affiliation:
FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
Email:
tf@noto.de
DOI:
10.1090/S0025-5718-03-01503-5
PII:
S 0025-5718(03)01503-5
Received by editor(s):
March 1, 2001
Received by editor(s) in revised form:
March 4, 2002
Posted:
February 3, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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