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Symbolic powers and matroids


Author: Matteo Varbaro
Journal: Proc. Amer. Math. Soc. 139 (2011), 2357-2366
MSC (2010): Primary 13A15, 05E45; Secondary 13A30
DOI: https://doi.org/10.1090/S0002-9939-2010-10685-8
Published electronically: December 8, 2010
MathSciNet review: 2784800
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Abstract: We prove that all the symbolic powers of a Stanley-Reisner ideal $ I_{\Delta}$ are Cohen-Macaulay if and only if the simplicial complex $ \Delta$ is a matroid.


References [Enhancements On Off] (What's this?)

  • [BCV] B. Benedetti, A. Constantinescu, M. Varbaro, Dimension, depth and zero-divisors of the algebra of basic $ k$-covers of a graph, Le Matematiche LXIII, n. II, pp. 117-156, 2008. MR 2531656 (2010c:13002)
  • [BH] W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 1993. MR 1251956 (95h:13020)
  • [BrVe] W. Bruns, U. Vetter, Determinantal rings, Lecture Notes in Mathematics, 1327, Springer-Verlag, 1988. MR 953963 (89i:13001)
  • [CV] A. Constantinescu, M. Varbaro, Koszulness, Krull dimension and other properties of graph-related algebra, available online at arXiv:1004.4980v1, 2010.
  • [HHT] J. Herzog, T. Hibi, N. V. Trung, Symbolic powers of monomial ideals and vertex cover algebras, Adv. in Math. 210, pp. 304-322, 2007. MR 2298826 (2007m:13005)
  • [Ly] G. Lyubeznik, On the local cohomology modules $ H_{\mathfrak{U}}^i(R)$ for ideals $ \mathfrak{U}$ generated by monomials in an $ R$-sequence, ``Complete Intersections'', Lect. Notes in Math., 1092, pp. 214-220, Springer, 1984. MR 775884 (86f:14002)
  • [MS] E. Miller, B. Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, 227, Springer-Verlag, 2005. MR 2110098 (2006d:13001)
  • [MT] N. C. Minh, N. V. Trung, Cohen-Macaulayness of powers of monomial ideals and symbolic powers of Stanley-Reisner ideals, available online at arXiv:1003.2152v1, 2010.
  • [NR] D.G. Northcott, D. Rees, Reduction of ideals in local rings, Proc. Cambridge Philos. Soc. 50, pp. 145-158, 1954. MR 0059889 (15:596a)
  • [Ox] J. G. Oxley, Matroid theory, Oxford University Press, 1992. MR 1207587 (94d:05033)
  • [St] R. P. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, 41, Birkhäuser Boston, 1996. MR 1453579 (98h:05001)
  • [TY] N. Terai, K. Yoshida, Locally complete intersection Stanley-Reisner ideals, Illinois J. Math. 53, pp. 413-429, 2009. MR 2594636
  • [We] D. J. A. Welsh, Matroid Theory, Academic Press, London, 1976. MR 0427112 (55:148)
  • [Ya] Z. Yan, An étale analog of the Goresky-Macpherson formula for subspace arrangements, J. Pure and App. Alg. 146, pp. 305-318, 2000. MR 1742346 (2000k:14041)

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Additional Information

Matteo Varbaro
Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Dodrcaneso 35, 16145, Genova, Italy
Email: varbaro@dima.unige.it

DOI: https://doi.org/10.1090/S0002-9939-2010-10685-8
Received by editor(s): March 14, 2010
Received by editor(s) in revised form: June 25, 2010
Published electronically: December 8, 2010
Communicated by: Irena Peeva
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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