Stanley–Reisner rings of simplicial complexes with a free action by an abelian group
Algebraic Combinatorics, Volume 1 (2018) no. 5, pp. 677-695.

We consider simplicial complexes admitting a free action by an abelian group. Specifically, we establish a refinement of the classic result of Hochster describing the local cohomology modules of the associated Stanley–Reisner ring, demonstrating that the topological structure of the free action extends to the algebraic setting. If the complex in question is also Buchsbaum, this new description allows for a specialization of Schenzel’s calculation of the Hilbert series of some of the ring’s Artinian reductions. In further application, we generalize to the Buchsbaum case the results of Stanley and Adin that provide a lower bound on the h-vector of a Cohen–Macaulay complex admitting a free action by a cyclic group of prime order.

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DOI: 10.5802/alco.29
Classification: 13F55,  05E45,  05E40
Keywords: Stanley–Reisner rings, local cohomology, group actions
Sawaske, Connor 1

1 Department of Mathematics University of Washington Seattle, WA 98195-4350, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Sawaske, Connor. Stanley–Reisner rings of simplicial complexes with a free action by an abelian group. Algebraic Combinatorics, Volume 1 (2018) no. 5, pp. 677-695. doi : 10.5802/alco.29. https://alco.centre-mersenne.org/articles/10.5802/alco.29/

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