论文标题
杜波伊斯奇点的纯子是du bois奇异性
Pure subrings of Du Bois singularities are Du Bois singularities
论文作者
论文摘要
令$ r \ to s $为Noetherian $ \ mathbb {q} $ - 代数的周期性纯映射。在本文中，我们表明，如果$ s $具有du bois奇点，那么$ r $就有杜波伊斯的奇异点。即使$ r \ to s $忠实地平坦，我们的结果也是新的。我们的证明在主要特征和混合特征方面也产生了有趣的结果。结果，我们表明，如果$ r \ to s $是循环纯净的环地图，基本上是有限数字上的有限数字的$ \ mathbb {c} $，$ s $具有log canonical型奇点，而$ k_r $是Cartier，那么$ r $ $ $ $ $具有log canonic canonical singularities。在途中，我们将Kovács和Schwede的密钥注射率定理扩展到具有均等特征零的任意Noetherian方案。在整个论文中，我们都使用复杂的$ \usewslineΩ^0_x $和Du Bois奇异性的表征，就Grothendieck拓扑而言。
Let $R \to S$ be a cyclically pure map of Noetherian $\mathbb{Q}$-algebras. In this paper, we show that if $S$ has Du Bois singularities, then $R$ has Du Bois singularities. Our result is new even when $R \to S$ is faithfully flat. Our proof also yields interesting results in prime characteristic and in mixed characteristic. As a consequence, we show that if $R \to S$ is a cyclically pure map of rings essentially of finite type over the complex numbers $\mathbb{C}$, $S$ has log canonical type singularities, and $K_R$ is Cartier, then $R$ has log canonical singularities. Along the way, we extend the key injectivity theorem of Kovács and Schwede to arbitrary Noetherian schemes of equal characteristic zero. Throughout the paper, we use the characterization of the complex $\underlineΩ^0_X$ and of Du Bois singularities in terms of sheafification with respect to Grothendieck topologies.
