Good ideals and $${p_{g}}$$ p g -ideals in two-dimensional normal singularities

Abstract

In this paper, we introduce the notion of $${p_{g}}$$ -ideals and $${p_{g}}$$ -cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we prove an existence of good ideals for two-dimensional Gorenstein normal local rings. Moreover, we classify all Ulrich ideals for two-dimensional simple elliptic singularities.