Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Topology of Equivariant Hilbert Schemes   For $G$ a finite group acting linearly on $\mathbb{A}^2$, the equivariant
Hilbert scheme $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ is a natural resolution
of singularities of $\operatorname{Sym}^r(\mathbb{A}^2/G)$. In this paper we
study the topology of $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ for abelian $G$
and how it depends on the group $G$. We prove that the topological invariants
of $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ are periodic or quasipolynomial in
the order of the group $G$ as $G$ varies over certain families of abelian
subgroups of $GL_2$. This is done by using the Bialynicki-Birula decomposition
to compute topological invariants in terms of the combinatorics of a certain
set of partitions.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn