Tokyo Journal of Mathematics

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

Nguyên Công MINH and Yukio NAKAMURA

Full-text: Open access

Abstract

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 $S/I^{(r)}$.

Article information

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

Dates
First available in Project Euclid: 11 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1313074452

Digital Object Identifier
doi:10.3836/tjm/1313074452

Mathematical Reviews number (MathSciNet)
MR2866644

Zentralblatt MATH identifier
1235.13017

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. 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. https://projecteuclid.org/euclid.tjm/1313074452


Export citation

References

  • W. Bruns and J. Herzog, Cohen-Macaulay rings, revised edition, Cambridge Univ. Press, Cambridge, 1998.
  • N. C. Minh and Y. Nakamura, The Buchsbaum property of symbolic powers of Stanley-Reisner ideals of dimension 1, J. Pure Appl. Algebra, 215 (2011), 161–167.
  • N. C. Minh and N. V. Trung, Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals, J. Algebra, 322 (2009), 4219–4227.
  • P. Schenzel, On the number of faces of simplicial complexes and the purity of Frobenius, Math. Z., 178 (1981), 125–142.
  • Y. Takayama, Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals, Bull. Math. Soc. Math. Roumanie (N. S.), 48 (96) (2005), 327–344.
  • Rafael H. Villarreal, Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics Vol. 238, Marcel Dekker, New York, 2001.