Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Eisenbud-Green-Harris Conjecture   It has been conjectured by Eisenbud, Green and Harris that if $I$ is a
homogeneous ideal in $k[x_1,...,x_n]$ containing a regular sequence
$f_1,...,f_n$ of degrees $\deg(f_i)=a_i$, where $2\leq a_1\leq ... \leq a_n$,
then there is a homogeneous ideal $J$ containing $x_1^{a_1},...,x_n^{a_n}$ with
the same Hilbert function. In this paper we prove the Eisenbud-Green-Harris
conjecture when $f_i$ splits into linear factors for all $i$.

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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: nlin