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

A. Buryak

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

Algebraic Geometry 2014-12-23 v2 Combinatorics

Authors: A. Buryak

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.

Keywords

quasihomogeneous Hilbert schemes Grothendieck ring q,t-Catalan numbers nested Hilbert schemes algebraic geometry

Cite

@article{arxiv.1011.4459,
  title  = {The classes of the quasihomogeneous Hilbert schemes of points on the plane},
  author = {A. Buryak},
  journal= {arXiv preprint arXiv:1011.4459},
  year   = {2014}
}

Comments

18 pages, published version

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