Nagoya Mathematical Journal

On the k-Buchsbaum property of powers of Stanley–Reisner ideals

Nguyên Công Minh and Yukio Nakamura

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Abstract

Let S=K[x1,x2,,xn] be a polynomial ring over a field K. Let Δ be a simplicial complex whose vertex set is contained in {1,2,,n}. For an integer k0, we investigate the k-Buchsbaum property of residue class rings S/I(t) and S/It for the Stanley–Reisner ideal I=IΔ. We characterize the k-Buchsbaumness of such rings in terms of the simplicial complex Δ and the power t. We also give a characterization in the case where I is the edge ideal of a simple graph.

Article information

Source
Nagoya Math. J., Volume 213 (2014), 127-140.

Dates
First available in Project Euclid: 17 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1387313477

Digital Object Identifier
doi:10.1215/00277630-2394073

Mathematical Reviews number (MathSciNet)
MR3161406

Zentralblatt MATH identifier
1291.13041

Subjects
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

Citation

Minh, Nguyên Công; Nakamura, Yukio. On the $k$ -Buchsbaum property of powers of Stanley–Reisner ideals. Nagoya Math. J. 213 (2014), 127--140. doi:10.1215/00277630-2394073. https://projecteuclid.org/euclid.nmj/1387313477


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