Tokyo Journal of Mathematics

A Note on the $k$-Buchsbaum Property of Symbolic Powers of Stanley-Reisner Ideals

Nguyên Công MINH and Yukio NAKAMURA

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Let $I$ be the Stanley-Reisner ideal of pure simplicial complex $\Delta$ of dimension one. We shall give a formula for $S/I^{(r)}$ to be a $k$-Buchsbaum ring for each $r>0$, where $I^{(r)}$ is the $r$-th symbolic power of $I$. The main result is an improvement of the previous result in [MN] on the $k$-Buchsbaumness of $S/I^{(r)}$.

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Tokyo J. Math., Volume 34, Number 1 (2011), 221-227.

First available in Project Euclid: 11 August 2011

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Zentralblatt MATH identifier

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10] 05E99: None of the above, but in this section


MINH, Nguyên Công; NAKAMURA, Yukio. A Note on the $k$-Buchsbaum Property of Symbolic Powers of Stanley-Reisner Ideals. Tokyo J. Math. 34 (2011), no. 1, 221--227. doi:10.3836/tjm/1313074452.

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