Moment angle complexes and big Cohen–Macaulayness

2012/05/31 by Shisen Luo, Tomoo Matsumura, W. Frank Moore · 10 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Cohomology ring #Combinatorics #Equivariant cohomology #Equivariant map #Geometry #Mathematics #Orbifold #Pure mathematics #Quotient #Ring (chemistry) #Toric variety #Torus #math.AC #math.AG #math.AT #math.SG #msc:14M25 #msc:55N91 #msc:57R18

paper · pdf · doi:10.2140/agt.2014.14.379

published in Algebraic & Geometric Topology 14(1), 379-406 (Mathematical Sciences Publishers) · 21 papges. Comments are welcome

arxiv created 2012/06/11 · openalex publication_date 2014/01/09 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let Z K C m be the moment angle complex associated to a simplicial complex K on OEm, together with the natural action of the torus T D U.1/ m . Let G T be a (possibly disconnected) closed subgroup and R WD T=G. Let ZOEK be the Stanley-Reisner ring of K and consider ZOER WD H .BRI Z/ as a subring of ZOET WD H .BTI Z/. We prove that H G .Z K I Z/ is isomorphic to Tor ZOER .ZOEK; Z/ as a graded module over ZOET

Citations

• Equivariant geometry and the cohomology of the moduli space of curves
• Commutative Ring Theory
• The integral cohomology of toric manifolds
• Cohomology rings of good contact toric manifolds
• Exact cohomology sequences with integral coefficients for torus actions
• Describing toric varieties and their equivariant cohomology
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Local Algebra