Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein Multiple Structures on Smooth Algebraic Varieties   We characterize the Gorenstein nilpotent scheme structures on a smooth
algebraic variety as support, in terms of a duality property of the graded
objects associated to two canonical filtrations.

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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
6
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: acc-phys
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas