Illinois Journal of Mathematics

Locally complete intersection Stanley–Reisner ideals

Naoki Terai and Ken-ichi Yoshida

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Abstract

In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension $\ge2$ that is locally complete intersection is a complete intersection ideal.

As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.

Article information

Source
Illinois J. Math., Volume 53, Number 2 (2009), 413-429.

Dates
First available in Project Euclid: 23 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1266934785

Digital Object Identifier
doi:10.1215/ijm/1266934785

Mathematical Reviews number (MathSciNet)
MR2594636

Zentralblatt MATH identifier
1186.13023

Subjects
Primary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Terai, Naoki; Yoshida, Ken-ichi. Locally complete intersection Stanley–Reisner ideals. Illinois J. Math. 53 (2009), no. 2, 413--429. doi:10.1215/ijm/1266934785. https://projecteuclid.org/euclid.ijm/1266934785


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