Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some algebraic consequences of Green's hyperplane restriction theorems   We discuss a paper of M. Green from a new algebraic perspective, and provide
applications of its results to level and Gorenstein algebras, concerning their
Hilbert functions and the weak Lefschetz property. In particular, we will
determine a new infinite class of symmetric $h$-vectors that cannot be
Gorenstein $h$-vectors, which was left open in a recent work of
Migliore-Nagel-Zanello. This includes the smallest example previously unknown,
$h=(1,10,9,10,1)$. As M. Green's results depend heavily on the characteristic
of the base field, so will ours. The appendix will contain a new argument,
kindly provided to us by M. Green, for Theorems 3 and 4 of his paper, since we
had found a gap in the original proof of those results during the preparation
of this manuscript.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex