The normal reduction number of two-dimensional cone-like singularities
The normal reduction number of two-dimensional cone-like singularities
复制标题
二维类锥奇点的法向约简数
DOI：
10.1090/proc/15565
复制
发表时间：
2021
影响因子：
1
通讯作者：
Ken-ichi
中科院分区：
文献类型：
--
作者：
Okuma;Tomohiro and Watanabe;Kei-ichi and Yoshida;Ken-ichi
取一个具有最小约化的正规二维局部环和一元一元闭理想。然后我们计算了数字：$\operatorname {nr}(I)=\min\{n\;|\;\overline {I^{n+ 1}}= Q\overline {I^ n}\},\quad\bar {r}(I)=\min\{n\;|\;\overline {I^{N+ 1}}= Q\overline {I^ N},\forall N\ge n\} $,，和，其中（resp.）是（resp.）的最大值。然后我们有这个，它是的几何属。本文给出了锥状奇点（异常集为单条光滑曲线的极小分辨率）的上界，并特别证明了它是由次次齐次多项式定义的超曲面奇点，则。我们还给出了一个and的例子，对于每个整数。参考文献
Letbe a normal two-dimensional local ring andan-primary integrally closed ideal with a minimal reduction. Then we calculate the numbers: $\operatorname {nr}(I)=\min\{n\;|\;\overline {I^{n+ 1}}= Q\overline {I^ n}\},\quad\bar {r}(I)=\min\{n\;|\;\overline {I^{N+ 1}}= Q\overline {I^ N},\forall N\ge n\} $,, and, where(resp.) is the maximum of(resp.) for all-primary integrally closed ideals. Then we have that, whereis the geometric genus of. In this paper, we give an upper bound ofwhenis a cone-like singularity (which has a minimal resolution whose exceptional set is a single smooth curve) and show, in particular, ifis a hypersurface singularity defined by a homogeneous polynomial of degree, then. Also we give an example ofandso thatbutfor every integer. References