Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearity Defects of Face Rings   Let $S = K[x_1, ..., x_n ]$ be a polynomial ring over a field $K$, and $E = K
< y_1, ..., y_n >$ an exterior algebra. The "linearity defect" $ld_E(N)$ of a
finitely generated graded $E$-module $N$ measures how far $N$ departs from
"componentwise linear". It is known that $ld_E(N) < \infty$ for all $N$. But
the value can be arbitrary large, while the similar invariant $ld_S(M)$ for an
$S$-module $M$ is alway at most $n$.
  We show that if $I_\Delta$ (resp. $J_\Delta$) is the squarefree monomial
ideal of $S$ (resp. $E$) corresponding to a simplicial complex $\Delta$ on ${1,
>..., n}$, then $ld_E(E/J_\Delta) = ld_S(S/I_\Delta)$. Moreover, except some
extremal cases, $ld$ is a topological invariant of the Alexander dual
$\Delta^\vee$ of $\Delta$.
  We also show that, when $n > 3$, $ld_E(E/J_\Delta) = n-2$ (this is the
largest possible value) if and only if $\Delta$ is an $n$-gon.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: cs
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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: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph