Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cup product for Hilbert schemes of points in the plane   We revisit Ellingsrud and Str{\o} mme's cellular decomposition of the Hilbert
scheme of points in the projective plane. We study the product of cohomology
classes defined by the closures of cells, deriving necessary conditions for the
non-vanishing of cohomology classes. Though our conditions are formulated in
purely combinatorial terms, the machinery for deriving them includes techniques
from Bia{\l} ynicki-Birula theory: We study closures of Bia{\l} ynicki-Birula
cells in complete complex varieties equipped with ample line bundles. We prove
a necessary condition for two such closures to meet, and apply this criterion
in our setting.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th