Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves   Let $\mathscr{I}$ be an ideal sheaf on $P^n$. In the first part of this
paper, we bound the asymptotic regularity of powers of $\mathscr{I}$ as
$ps-3\leq \reg \mathscr{I}^p\leq ps+e$, where $e$ is a constant and $s$ is the
$s$-invariant of $\mathscr{I}$. We also give the same upper bound for the
asymptotic regularity of symbolic powers of $\mathscr{I}$ under some
conditions. In the second part, by using multiplier ideal sheaves, we give a
vanishing theorem of powers of $\mathscr{I}$ when it defines a local complete
intersection subvariety with log canonical singularities.

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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph