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 -vector of a Cohen–Macaulay complex admitting a free action by a cyclic group of prime order.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.29
Keywords: Stanley–Reisner rings, local cohomology, group actions
@article{ALCO_2018__1_5_677_0, author = {Sawaske, Connor}, title = {Stanley{\textendash}Reisner rings of simplicial complexes with a free action by an abelian group}, journal = {Algebraic Combinatorics}, pages = {677--695}, publisher = {MathOA foundation}, volume = {1}, number = {5}, year = {2018}, doi = {10.5802/alco.29}, mrnumber = {3887407}, zbl = {06987762}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.29/} }
TY - JOUR AU - Sawaske, Connor TI - Stanley–Reisner rings of simplicial complexes with a free action by an abelian group JO - Algebraic Combinatorics PY - 2018 SP - 677 EP - 695 VL - 1 IS - 5 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.29/ DO - 10.5802/alco.29 LA - en ID - ALCO_2018__1_5_677_0 ER -
%0 Journal Article %A Sawaske, Connor %T Stanley–Reisner rings of simplicial complexes with a free action by an abelian group %J Algebraic Combinatorics %D 2018 %P 677-695 %V 1 %N 5 %I MathOA foundation %U http://archive.numdam.org/articles/10.5802/alco.29/ %R 10.5802/alco.29 %G en %F 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. http://archive.numdam.org/articles/10.5802/alco.29/
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