# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## Non-Cohen-Macaulay symbolic blow-ups for space monomial curvesHTML articles powered by AMS MathViewer

by Mayumi Morimoto and Shiro Goto
Proc. Amer. Math. Soc. 116 (1992), 305-311 Request permission

## Abstract:

Let $\mathfrak {p} = \mathfrak {p}({n_1},{n_2},{n_3})$ denote the prime ideal in the formal power series ring $A = k[[X,Y,Z]]$ over a field $k$ defining the space monomial curve $X = {T^{{n_1}}},Y = {T^{{n_2}}}$, and $Z = {T^{{n_3}}}$ with $\operatorname {GCD} ({n_1},{n_2},{n_3}) = 1$. Then the symbolic Rees algebra ${R_s}(\mathfrak {p}) = { \oplus _{n \geq 0}}{\mathfrak {p}^{(n)}}$ for $\mathfrak {p} = \mathfrak {p}({n^2} + 2n + 2,{n^2} + 2n + 1,{n^2} + n + 1)$ is Noetherian but not Cohen-Macaulay if ${\text {ch}}k = p > 0$ and $n = {p^e}$ with $e \geq 1$. The same is true for $\mathfrak {p} = \mathfrak {p}({n^2},{n^2} + 1,{n^2} + n + 1)$ if ${\text {ch}}k = p > 0$ and $n = {p^e} \geq 3$ .
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