Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal Containments under Flat Extensions   Let $\varphi : S = k[y_0,..., y_n] \to R = k[y_0,...,y_n]$ be given by $y_i
\to f_i$ where $f_0,...,f_n$ is an $R$-regular sequence of homogeneous elements
of the same degree. A recent paper shows for ideals, $I_\Delta \subseteq S$, of
matroids, $\Delta$, that $I_\Delta^{(m)} \subseteq I^r$ if and only if
$\varphi_*(I_\Delta)^{(m)} \subseteq \varphi_*(I_\Delta)^r$ where
$\varphi_*(I_\Delta)$ is the ideal generated in $R$ by $\varphi(I_\Delta)$. We
prove this result for saturated homogeneous ideals $I$ of configurations of
points in $\mathbb{P}^n$ and use it to obtain many new counterexamples to
$I^{(rn - n + 1)} \subseteq I^r$ from previously known counterexamples.

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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph