Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Formula for the Core of Certain Strongly Stable Ideals   The core of an ideal is the intersection of all of its reductions. The core
has geometric significance coming, for example, from its connection to adjoint
and multiplier ideals. In general, though, the core is difficult to describe
explicitly. In this paper, we investigate a particular family of strongly
stable ideals. We prove that ideals in this family satisfy an Artin-Nagata
property, yet fail to satisfy other, stronger standard depth conditions. We
then show that there is a surprisingly simple explicit formula for the core of
these ideals.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn