A linear variant of the nearly Gorenstein property

2024/07/08 by Miyashita, Sora · 2 citations
#05E40 #13A02 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13H10 #Secondary 14M25

paper · doi:10.48550/arxiv.2407.05629

Abstract

We introduce a condition (\natural) for Cohen--Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. In this context, condition (\natural) is characterized by a Minkowski decomposition of certain lattice polytopes. We show that if R satisfies (\natural), then its Veronese subrings R^(k) are nearly Gorenstein for all sufficiently large k. This extends previously known results on Ehrhart rings and shows that condition (\natural) provides a valuable framework from both ring-theoretic and combinatorial perspectives.

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