Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groebner bases for spaces of quadrics of codimension 3   Let $R=\oplus_{i\geq 0} R_i$ be an Artinian standard graded $K$-algebra
defined by quadrics. Assume that $\dim R_2\leq 3$ and that $K$ is algebraically
closed of characteristic $\neq 2$. We show that $R$ is defined by a Gr\"obner
basis of quadrics with, essentially, one exception. The exception is given by
$K[x,y,z]/I$ where $I$ is a complete intersection of 3 quadrics not containing
the square of a linear form.

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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
6
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: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: alg-geom