Abstract
Let be the moment angle complex associated to a simplicial complex on , together with the natural action of the torus . Let be a (possibly disconnected) closed subgroup and . Let be the Stanley–Reisner ring of and consider as a subring of . We prove that is isomorphic to as a graded module over . Based on this, we characterize the surjectivity of (ie ) in terms of the vanishing of and discuss its relation to the freeness and the torsion-freeness of over . For various toric orbifolds , by which we mean quasitoric orbifolds or toric Deligne–Mumford stacks, the cohomology of can be identified with with appropriate and and the above results mean that and that if and only if is the quotient .
Citation
Shisen Luo. Tomoo Matsumura. W Frank Moore. "Moment angle complexes and big Cohen–Macaulayness." Algebr. Geom. Topol. 14 (1) 379 - 406, 2014. https://doi.org/10.2140/agt.2014.14.379
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