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Higher Cohen-Macaulay property of squarefree modules and simplicial posets


Author: Kohji Yanagawa
Journal: Proc. Amer. Math. Soc. 139 (2011), 3057-3066
MSC (2010): Primary 13F55, 13C14; Secondary 55U10
DOI: https://doi.org/10.1090/S0002-9939-2011-10734-2
Published electronically: January 19, 2011
MathSciNet review: 2811262
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, G. Fløystad studied higher Cohen-Macaulay property of certain finite regular cell complexes. In this paper, we partially extend his results to squarefree modules, toric face rings, and simplicial posets. For example, we show that if (the corresponding cell complex of) a simplicial poset is $ l$-Cohen-Macaulay, then its codimension one skeleton is $ (l+1)$-Cohen-Macaulay.


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

  • 1. C.A. Athanasiadis and V. Welker, Buchsbaum* complexes, preprint (arXiv:0909.1931).
  • 2. K. Baclawski, Cohen-Macaulay connectivity and geometric lattices, Europ. J. Combinatorics 3 (1982), 293-305. MR 687728 (84d:06001)
  • 3. W. Bruns and J. Gubeladze, Polytopes, rings, and $ K$-theory, Springer, 2009. MR 2508056 (2010d:19001)
  • 4. W. Bruns and J. Herzog, Cohen-Macaulay rings, revised edition, Cambridge University Press, 1998. MR 1251956 (95h:13020)
  • 5. W. Bruns, R. Koch, and T. Römer, Gröbner bases and Betti numbers of monoidal complexes, Michigan Math. J. 57 (2008), 71-91. MR 2492442 (2010a:13045)
  • 6. A.M. Duval, Free resolutions of simplicial posets, J. Algebra 188 (1997), 363-399. MR 1432361 (97m:13031)
  • 7. E. G. Evans and P. Griffith, Syzygies, London Mathematical Society Lecture Note Series, vol. 106, 1985. MR 811636 (87b:13001)
  • 8. G. Fløystad, Cohen-Macaulay cell complexes, in Algebraic and Geometric Combinatorics, C. A. Athanasiadis et al., eds., Contemporary Mathematics, vol. 423, American Mathematical Society, 2007, pp. 205-220. MR 2298759 (2008h:13036)
  • 9. B. Ichim and T. Römer, On toric face rings, J. Pure Appl. Algebra 210 (2007), 249-266. MR 2311184 (2008a:13032)
  • 10. E. Miller, The Alexander duality functors and local duality with monomial support, J. Algebra 231 (2000), 180-234. MR 1779598 (2001k:13028)
  • 11. R. Okazaki and K. Yanagawa, Dualizing complex of a toric face ring, Nagoya Math. J. 196 (2009), 87-116. MR 2591092
  • 12. T. Römer, Generalized Alexander duality and applications, Osaka J. Math. 38 (2001), 469-485. MR 1833633 (2002c:13029)
  • 13. R. Stanley, $ f$-vectors and $ h$-vectors of simplicial posets, J. Pure Appl. Algebra 71 (1991), 319-331. MR 1117642 (93b:06009)
  • 14. R. Stanley, Combinatorics and commutative algebra, 2nd ed., Birkhäuser, 1996. MR 1453579 (98h:05001)
  • 15. K. Yanagawa, Alexander duality for Stanley-Reisner rings and squarefree $ \mathbb{N}^n$-graded modules, J. Algebra 225 (2000), 630-645. MR 1741555 (2000m:13036)
  • 16. K. Yanagawa, Derived category of squarefree modules and local cohomology with monomial ideal support, J. Math. Soc. Japan 56 (2004), 289-308. MR 2028674 (2004j:13041)
  • 17. K. Yanagawa, Dualizing complex of the face ring of a simplicial poset, preprint (arXiv:0910.1498).

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Additional Information

Kohji Yanagawa
Affiliation: Department of Mathematics, Kansai University, Suita 564-8680, Japan
Email: yanagawa@ipcku.kansai-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2011-10734-2
Keywords: Simplicial complex, regular cell complex, higher Cohen-Macaulay, doubly Cohen-Macaulay, squarefree module, toric face ring, simplicial poset
Received by editor(s): January 26, 2010
Received by editor(s) in revised form: August 7, 2010
Published electronically: January 19, 2011
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (c) (no. 19540028).
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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