Abstract
Abstract: In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of -quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the -Catalan numbers. Finally, we investigate a connection between -quasi-homogeneous Hilbert schemes and homogeneous nested Hilbert schemes. Key words and phrases: Hilbert scheme, torus action, -Catalan numbers.
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