Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and Koszul property of symbolic powers of monomial ideals   Let $I$ be a homogeneous ideal in a polynomial ring over a field. Let
$I^{(n)}$ be the $n$-th symbolic power of $I$. Motivated by results about
ordinary powers of $I$, we study the asymptotic behavior of the regularity
function $\text{reg}~ (I^{(n)})$ and the maximal generating degree function
$\omega(I^{(n)})$, when $I$ is a monomial ideal. It is known that both
functions are eventually quasi-linear. We show that, in addition, the sequences
$\{\text{reg}~ I^{(n)}/n\}_n$ and $\{\omega(I^{(n)})/n\}_n$ converge to the
same limit, which can be described combinatorially. We construct an example of
an equidimensional, height two squarefree monomial ideal $I$ for which
$\omega(I^{(n)})$ and $\text{reg}~ (I^{(n)})$ are not eventually linear
functions. For the last goal, we introduce a new method for establishing the
componentwise linearity of ideals. This method allows us to identify a new
class of monomial ideals whose symbolic powers are componentwise linear.

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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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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: nucl-th