论文标题
链接和$ f $ - 确定戒指的限制性
Linkage and $F$-Regularity of Determinantal Rings
论文作者
论文摘要
在本文中，我们证明由最大未成年人定义的通用确定环的通用链接非常强烈。在此过程中，我们在分级环境中加强了霞多丽和乌尔里希的结果。他们表明，完整的交点环与理性概念的通用残差相交再次具有理性的概念。我们表明，如果所述完整的交叉路口由均质元素定义并且是$ f $ - 理性的，那么实际上，其通用的剩余交集在正面的主要特征上是强烈的$ f $ rengular。 Hochster和Huneke表明，确定戒指强烈$ f $ groumar；但是，他们的证据很涉及。我们的技术使我们能够提供一个新的简单证明，证明最大未成年人定义的确定性环的强大$ f $ reformunity。
In this paper, we prove that the generic link of a generic determinantal ring defined by maximal minors is strongly $F$-regular. In the process, we strengthen a result of Chardin and Ulrich in the graded setting. They showed that the generic residual intersections of a complete intersection ring with rational singularities again have rational singularities. We show that if the said complete intersection is defined by homogeneous elements and is $F$-rational, then in fact, its generic residual intersections are strongly $F$-regular in positive prime characteristic. Hochster and Huneke showed that determinantal rings are strongly $F$-regular; however, their proof is quite involved. Our techniques allow us to give a new and simple proof of the strong $F$-regularity of determinantal rings defined by maximal minors.
