A hierarchy of parametrizing varieties for representations

  • B. Huisgen-Zimmermann, Barbara Osofsky
  • Published 2008


The primary purpose is to introduce and explore projective varieties, grassd(Λ), parametrizing the full collection of those modules over a finite dimensional algebra Λ which have dimension vector d. These varieties extend the smaller varieties previously studied by the author; namely, the projective varieties encoding those modules with dimension vector d which, in addition, have a preassigned top or radical layering. Each of the grassd(Λ) 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.

Cite this paper

@inproceedings{HuisgenZimmermann2008AHO, title={A hierarchy of parametrizing varieties for representations}, author={B. Huisgen-Zimmermann and Barbara Osofsky}, year={2008} }