Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
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正规二维奇点中的正规希尔伯特系数和椭圆理想
DOI：
10.1017/nmj.2022.5
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发表时间：
2022
影响因子：
0.8
通讯作者：
Ken-ichi
中科院分区：
文献类型：
--
作者：
Okuma;Tomohiro and Rossi;Maria Evelina and Watanabe;Kei-ichi and Yoshida;Ken-ichi
设是一个优良的二维正规局部区域。本文根据Wgreich和Yau给出的定义，研究了A的椭圆理想和强椭圆理想，目的是刻画椭圆和强椭圆奇点。与有理奇点类似，在主要结果中，我们用A的积分闭素理想的正规Hilbert系数刻画了强椭圆奇点。不同于理想，椭圆理想和强椭圆理想不一定是正规的和必要的，并给出了正规的充分条件。在最后一节中，我们讨论了任意二维正规局部环中强椭圆理想的存在性(及其有效构造)。
Let be an excellent two-dimensional normal local domain. In this paper, we study the elliptic and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and Yau. In analogy with the rational singularities, in the main result, we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed -primary ideals of A. Unlike -ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary, and sufficient conditions for being normal are given. In the last section, we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.