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arXiv · 1511.00827

Rees algebras and $p_g$-ideals in a two-dimensional normal local domain

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

The authors introduced the notion of $p_g$-ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In this note, we give several ring-theoretic characterization of $p_g$-ideals. For instance, an $m$-primary ideal $I \subset A$ is a $p_g$-ideal if and only if the Rees alegbra $\mathcal{R}(I)$ is a Cohen-Macaulay normal domain.

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Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida. 2015-11-03. Rees algebras and $p_g$-ideals in a two-dimensional normal local domain. https://doi.org/10.1090/proc%2F13235

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