  Non-commutative Hilbert schemes, introduced by M. V. Nori, parametrize left
ideals of finite codimension in free algebras. More generally, parameter spaces
of finite codimensional submodules of free modules over free algebras are
considered. Cell decompositions of these varieties are constructed, whose cells
are parametrized by certain types of forests. Asymptotics for the corresponding
Poincare polynomials and properties of their generating functions are
discussed.

Algebraic Geometry;Rings and Algebras