  Let I be a finite set and CI be the algebra of functions on I. For a finite
dimensional C algebra A with \CI contained in A we show that certain moduli
spaces of finite dimsional modules are isomorphic to certain Grassmannian
(quot-type) varieties. There is a special case of interest in representation
theory. Lusztig defined two varieties related to a quiver and gave a bijection
between their C-points (citation in article). Savage and Tingley raised the
question (citation in article) of whether these varieties are isomorphic as
algebraic varieties. This question has been open since Lusztig's original work.
It follows from the result of this note that the two varieties are indeed
isomorphic.
