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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
Published electronically: January 19, 2011
MathSciNet review: 2811262
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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.

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Additional Information

Kohji Yanagawa
Affiliation: Department of Mathematics, Kansai University, Suita 564-8680, Japan

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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