Cohomology of non-commutative Hilbert schemes
Abstract
Description
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.
22 pages; some comments and references added; more on asymptotics of Euler numbers and Poincare polynomials
22 pages; some comments and references added; more on asymptotics of Euler numbers and Poincare polynomials