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arXiv · 1407.1590

Good ideals and $p_g$-ideals in two-dimensional normal singularities

Tomohiro Okuma·Kei-ichi Watanabe·Ken-ichi Yoshida
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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.

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Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida. 2014-07-07. Good ideals and $p_g$-ideals in two-dimensional normal singularities. https://doi.org/10.1007/s00229-016-0821-7

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