2022/12/03 by Laura Felicia Matusevich, Matusevich, Laura Felicia, Erika Ordog +3
Mathematics · #13D45 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13F65 #Secondary 13F55
paper · pdf · doi:10.48550/arxiv.2212.01511
openalex publication_date 2022/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a generalize Ishida complex to compute the local cohomology with monomial support of modules over quotients of polynomial rings by cellular binomial ideals. As a consequence, we obtain a combinatorial criterion to determine when such a quotient is Cohen--Macaulay. In particular, this gives a Cohen--Macaulayness criterion for lattice ideals. We also prove a result relating the local cohomology with radical monomial ideal support of an affine semigroup ring to the local cohomology with maximal ideal support of the quotient of the affine semigroup ring by the radical monomial ideal. This requires a combinatorial assumption on the semigroup, which holds for (not necessarily normal) semigroups whose cone is the cone over a simplex.