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arXiv · 1011.4459

The classes of the quasihomogeneous Hilbert schemes of points on the plane

A. Buryak
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Abstract

In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of $(1,k)$-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the $q,t$-Catalan numbers. Finally, we investigate a connection between $(1,k)$-quasi-homogeneous Hilbert schemes and homogeneous nested Hilbert schemes.

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A. Buryak. 2010-11-19. The classes of the quasihomogeneous Hilbert schemes of points on the plane. https://arxiv.org/abs/1011.4459

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