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

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

2010-11-19

arxiv.org/abs/1011.4459v1

Mathematics

Algebraic Geometry

Scientific paper

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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