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A hierarchy of parametrizing varieties for representations
The primary purpose is to introduce and explore projective varieties,
, parametrizing the full collection of those
modules over a finite dimensional algebra which have dimension vector
. These varieties extend the smaller varieties previously studied by the
author; namely, the projective varieties encoding those modules with dimension
vector which, in addition, have a preassigned top or radical layering.
Each of the is again partitioned by the action
of a linear algebraic group, and covered by certain
representation-theoretically defined affine subvarieties which are stable under
the unipotent radical of the acting group. A special case of the pertinent
theorem served as a cornerstone in the work on generic representations by
Babson, Thomas, and the author. Moreover, applications are given to the study
of degenerations