Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criteria for componentwise linearity   We establish characteristic-free criteria for the componentwise linearity of
graded ideals. As applications, we classify the componentwise linear ideals
among the Gorenstein ideals, the standard determinantal ideals, and the ideals
generated by the submaximal minors of a symmetric matrix.

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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio