Cohomology of non-commutative Hilbert schemes

Abstract

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

References in corpus (1)

• Canonical systems and non-commutative geometry

Cited by in corpus (8)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Moduli of representations of quivers
• Smooth models of quiver moduli
• Hilbert schemes of points for associative algebras
• Framed quiver moduli, cohomology, and quantum groups
• The superpotential $XYZ+XZY+\frac{c}{3}(X^3+Y^3+Z^3)$
• Moduli of linear representations, symmetric products and the non commutative Hilbert scheme
• Hilbert-Chow morphism for non commutative Hilbert schemes and moduli spaces of linear representations