A characterization of two-dimensional rational singularities via core of ideals

作者：Okuma Tomohiro^*; Watanabe Kei ichi; Yoshida Ken ichi

来源：Journal of Algebra, 2018, 499: 450-468.

DOI：10.1016/j.jalgebra.2017.11.053

• Core of ideals
• Good ideal
• p(g)-cycle
• p(g)-ideal
• Surface singularity
• Rational singularity

The notion of p(g)-ideals for normal surface singularities has been proved to be very useful. On the other hand, the core of ideals has been proved to be very important concept and also very mysterious one. However, the computation of the core of an ideal seems to be given only for very special cases. In this paper, we will give an explicit description of the core of p(g)-ideals of normal surface singularities. As a consequence, we give a characterization of rational singularities using the inclusion of the core of integrally closed ideals.

• 出版日期2018-4-1