Good ideals and $p_g$-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 with small degree.

21 pages. The proof of Proposition 5.6 of the first version has been revised

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• Gorensteinness for normal tangent cones of elliptic ideals
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