Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 1 (2014), 379-406.
Moment angle complexes and big Cohen–Macaulayness
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 .
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 379-406.
Received: 5 August 2012
Revised: 10 March 2013
Accepted: 28 May 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55N91: Equivariant homology and cohomology [See also 19L47]
Secondary: 57R18: Topology and geometry of orbifolds 53D20: Momentum maps; symplectic reduction 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Luo, Shisen; Matsumura, Tomoo; Moore, W Frank. Moment angle complexes and big Cohen–Macaulayness. Algebr. Geom. Topol. 14 (2014), no. 1, 379--406. doi:10.2140/agt.2014.14.379. https://projecteuclid.org/euclid.agt/1513715805