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

Abstract

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.

16 pages; various corrections and improvements. To appear in Journal of Algebra

References in corpus (2)

• A formula for the core of an ideal
• Rees algebras and $p_g$-ideals in a two-dimensional normal local domain

Cited by in corpus (7)

• Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type
• Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
• Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals
• Cohomology of ideals in elliptic surface singularities
• The normal reduction number of two-dimensional cone-like singularities
• The core of a module and the adjoint of an ideal over a two dimensional regular local ring
• Normal reduction numbers of normal surface singularities