Rees algebras and 𝑝_{𝑔}-ideals in a two-dimensional normal local domain

Okuma, Tomohiro; Watanabe, Kei-ichi; Yoshida, Ken-ichi

doi:10.1090/proc/13235

Rees algebras and $p_g$-ideals in a two-dimensional normal local domain
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by Tomohiro Okuma, Kei-ichi Watanabe and Ken-ichi Yoshida PDF

Proc. Amer. Math. Soc. 145 (2017), 39-47 Request permission

Abstract:

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

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