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.

arXiv comment22 pages; some comments and references added; more on asymptotics of Euler numbers and Poincare polynomials

References in corpus (2)

• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
• Canonical systems and non-commutative geometry

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