Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of multiplicities of graded families of ideals   Let $(R,\mathfrak{m})$ be a Noetherian local ring of dimension $d > 0$. Let
$I_\bullet = \{I_n\}_{n \in \mathbb{N}}$ be a graded family of
$\mathfrak{m}$-primary ideals in $R$. We examine how far off from a polynomial
can the length function $\ell_R(R/I_n)$ be asymptotically. More specifically,
we show that there exists a constant $\gamma > 0$ such that for all $n \ge 0$,
$$\ell_R(R/I_{n+1}) - \ell_R(R/I_n) < \gamma n^{d-1}.$$

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg