 
Summary: Contemporary Mathematics
Volume 00, 1997
A hierarchy of parametrizing varieties for representations
B. HuisgenZimmermann
Dedicated to Carl Faith and Barbara Osofsky
Abstract. The primary purpose is to introduce and explore projective va
rieties, grassd(), parametrizing the full collection of those modules over a
finite dimensional algebra which have dimension vector d. These varieties
extend the smaller varieties previously studied by the author; namely, the pro
jective varieties encoding those modules with dimension vector d which, in
addition, have a preassigned top or radical layering. Each of the grassd()
is again partitioned by the action of a linear algebraic group, and covered by
certain representationtheoretically defined affine subvarieties which are stable
under the unipotent radical of the acting group. A special case of the perti
nent 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.
1. Introduction and notation
Our primary aim is to extend some of the concepts, constructions and results
from [8], [9], and [1] for wider applicability towards exploring the representation
