Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic Samuel function and invariants of singularities   The asymptotic Samuel function generalizes to arbitrary rings the usual order
function of a regular local ring. In this paper, we use this function to define
the "Samuel slope" of a Noetherian local ring, and we study some of its
properties. In addition, we focus on the case of a local ring at a singular
point of a variety, and, among other results, we prove that the Samuel slope of
these rings is related to some invariants used in algorithmic resolution of
singularities.

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The categories of this paper are: stat
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph