Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Containment problem for points on a reducible conic in $\mathbb{P}^2$   Given an ideal $I$ in a Noetherian ring, one can ask the containment
question: for which $m$ and $r$ is the symbolic power $I^{(m)}$ contained in
the ordinary power $I^r$? C. Bocci and B. Harbourne study the containment
question in a geometric setting, where the ideal $I$ is in a polynomial ring
over a field. Like them, we will consider special geometric constructs. In
particular, we obtain a complete solution in two extreme cases of ideals of
points on a pair of lines in $\mathbb{P}^2$; in one case, the number of points
on each line is the same, while in the other all the points but one are on one
of the lines.

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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom