by SmalØ, S. O.; Valenta, A.

Let Λ be a finitely generated associative k-algebra where k is an algebraically closed field. For each natural number d, we have the variety of d-dimensional module structures on kd given by the multiplication of the elements from a generating set of Λ. The general linear group Gld(k) acts on this variety by conjugation and the orbits under this action correspond to isomorphism classes of d-dimensional Λ-modules. For two d-dimensional Λ-modules M and N one says that M degenerates to N if the orbit corresponding to N is in the Zariski-closure of the orbit corresponding to M. Now in this situation the stabilizers of the elements in the orbit corresponding to N acts on the orbit corresponding to M.

In this paper we characterize degenerations of k[t]/(tr)-modules with the property that for each y in the orbit corresponding to N, there is an xy in the orbit corresponding to M such that the orbit corresponding to M is the disjoint union of orbits of the xy’s under the action of the stabilizer of y where y runs through the orbit corresponding to N.

DOI: 10.1007/s10468-005-3604-5
Print publication date: 5/1/2005
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