# ALGEBRAIC COMBINATORICS

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.

Revised: 2018-05-18
Accepted: 2018-06-20
Published online: 2018-11-30
DOI: https://doi.org/10.5802/alco.29
Classification: 13F55,  05E45,  05E40
Keywords: Stanley–Reisner rings, local cohomology, group actions
@article{ALCO_2018__1_5_677_0,
title = {Stanley--Reisner rings of simplicial complexes with a free action by an abelian group},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {1},
number = {5},
year = {2018},
pages = {677-695},
doi = {10.5802/alco.29},
mrnumber = {3887407},
zbl = {06987762},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2018__1_5_677_0/}
}
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/item/ALCO_2018__1_5_677_0/

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