2021/04/08 by Matthias Franz, Franz, Matthias, Xin Fu +1
Mathematics · #14F45 #14M25 #55N91 (Secondary) #57S12 (Primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2104.03825
openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building on the recent computation of the cohomology rings of smooth toric varieties and partial quotients of moment-angle complexes, we investigate the naturality properties of the resulting isomorphism between the cohomology of such a space and the torsion product involving the Stanley-Reisner ring. If 2 is invertible in the chosen coefficient ring, then the isomorphism is natural with respect to toric morphisms, which for partial quotients are defined in analogy with toric varieties. In general there are deformation terms that we describe explicitly.