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摘要翻译：
设$O_x$(resp.$D_x$)是$x$(=复仿射n-空间）上的全纯函数簇（resp.n-空间上的具有全纯系数的线性微分算子簇）。设$y$是由多项式$f$定义的局部弱拟齐次自由因子。本文局部证明了$1/f^k$上$d_x$的湮没理想是由1阶线性微分算子生成的（对于$k$足够大）。为此，我们证明了对数$D_x$-模的扩张群的一个消失定理。对数的$d_x$--模块自然与$y$相关联。这个结果与所谓的对数比较定理有关。
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英文标题：
《A vanishing theorem for a class of logarithmic D-modules》
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作者：
F.J. Castro-Jimenez (1), J. Gago (1), M.I. Hartillo-Hermoso (2) and
J.M. Ucha (1)((1) University of Seville, (2) University of Cadiz)
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0707.1000
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