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


Authors: Tomohiro Okuma, Kei-ichi Watanabe and Ken-ichi Yoshida
Journal: Proc. Amer. Math. Soc. 145 (2017), 39-47
MSC (2010): Primary 13B22; Secondary 13A30, 14B05
DOI: https://doi.org/10.1090/proc/13235
Published electronically: June 30, 2016
MathSciNet review: 3565358
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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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Additional Information

Tomohiro Okuma
Affiliation: Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, 990-8560, Japan
Email: okuma@sci.kj.yamagata-u.ac.jp

Kei-ichi Watanabe
Affiliation: Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 156-8550, Japan
Email: watanabe@math.chs.nihon-u.ac.jp

Ken-ichi Yoshida
Affiliation: Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 156-8550, Japan
Email: yoshida@math.chs.nihon-u.ac.jp

DOI: https://doi.org/10.1090/proc/13235
Keywords: $p_g$-ideal, Rees algebra, normal Hilbert coefficient, Cohen-Macaulay, rational singularity
Received by editor(s): October 30, 2015
Received by editor(s) in revised form: March 5, 2016
Published electronically: June 30, 2016
Additional Notes: This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Numbers, 25400050, 26400053, 26400064
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society