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Mathematics > Commutative Algebra

arXiv:2211.10577 (math)
[Submitted on 19 Nov 2022]

Title:Graded local cohomology of modules over semigroup rings

Authors:Byeongsu Yu, Laura Felicia Matusevich
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Abstract:We give a combinatorial description of local cohomology modules of a graded module over a semigroup ring, with support at the graded maximal ideal. This combinatorial framework yields Hochster-type formulas for the Hilbert series of such local cohomology modules in terms of the homology of finitely many polyhedral cell complexes. A Cohen--Macaulay criterion immediately follows. We also provide an alternative proof of a result of [18] characterizing Cohen--Macaulay affine semigroup rings.
Comments: 21 pages, 4 figures
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO)
MSC classes: 13D45, 13F65, 05E40, 20M25 (Primary) 13C14, 13F55, 14M25, 52B20 (Secondary)
Cite as: arXiv:2211.10577 [math.AC]
  (or arXiv:2211.10577v1 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.2211.10577

Submission history

From: Byeongsu Yu [view email]
[v1] Sat, 19 Nov 2022 03:47:04 UTC (29 KB)
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