TL;DR
This paper studies punctual noncommutative Hilbert schemes, focusing on their geometric and topological properties by computing motives and intersection cohomology through affine pavings and resolutions.
Contribution
It provides the first detailed analysis of motives and intersection cohomology for punctual noncommutative Hilbert schemes, including explicit constructions of affine pavings and resolutions.
Findings
Motives of punctual noncommutative Hilbert schemes are explicitly determined.
Intersection cohomology is computed using affine pavings.
Small resolutions of singularities are constructed for these schemes.
Abstract
Punctual noncommutative Hilbert schemes are projective varieties parametrizing finite codimensional left ideals in noncommutative formal power series rings. We determine their motives and intersection cohomology, by constructing affine pavings and small resolutions of singularities.
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