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摘要翻译：
我们证明了Cohen-Macaulay正规簇$x$具有Du Bois奇点当且仅当$\pi_*\omega_{x'}(G)\simeq\omega_x$对于一个对数分辨率$\pi:x'\到x$,其中$G$是$\pi$的约化例外因子。许多关于Du Bois奇点的基本定理通过这种刻画变得透明（包括Cohen-Macaulay对数正则奇点是Du Bois的事实）。在Cohen-Macaulay情形下，我们也给出了半对数正则奇点的推广是Du Bois的一个直接的、自包含的证明。本文还证明了Kodaira消失定理对半对数正则簇成立，Cohen-Macaulay半对数正则奇点在Dolgachev意义下是上同调的不重要的。
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英文标题：
《The canonical sheaf of Du Bois singularities》
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作者：
S\'andor J. Kov\'acs, Karl E. Schwede, Karen E. Smith
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最新提交年份：
2010
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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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一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
We prove that a Cohen-Macaulay normal variety $X$ has Du Bois singularities if and only if $\pi_*\omega_{X'}(G) \simeq \omega_X$ for a log resolution $\pi: X' \to X$, where $G$ is the reduced exceptional divisor of $\pi$. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward and self-contained proof that (generalizations of) semi-log-canonical singularities are Du Bois, in the Cohen-Macaulay case. It also follows that the Kodaira vanishing theorem holds for semi-log-canonical varieties and that Cohen-Macaulay semi-log-canonical singularities are cohomologically insignificant in the sense of Dolgachev.
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PDF链接：
https://arxiv.org/pdf/0801.1541
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