Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A vanishing theorem for a class of logarithmic D-modules   Let $O_X$ (resp. $D_X$) be the sheaf of holomorphic functions (resp. the
sheaf of linear differential operators with holomorphic coefficients) on $X$
(=the complex affine n-space). Let $Y$ be a locally weakly quasi-homogeneous
free divisor defined by a polynomial $f$. In this paper we prove that, locally,
the annihilating ideal of $1/f^k$ over $D_X$ is generated by linear
differential operators of order 1 (for $k$ big enough). For this purpose we
prove a vanishing theorem for the extension groups of a certain logarithmic
$D_X$--module with $O_X$. The logarithmic $D_X$--module is naturally associated
with $Y$. This result is related to the so called Logarithmic Comparison
Theorem.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex