A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras

Sora Miyashita

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arXiv · 2407.05629

A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras

Sora Miyashita

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Abstract

We studies the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition~$(\natural)$ for Cohen--Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi-standard graded algebra $ R $ satisfies~$(\natural)$, then its Veronese subalgebras $ R^{(k)} $ are nearly Gorenstein for all sufficiently large $ k $. We also prove that if a standard graded algebra $R$ is nearly Gorenstein so does its Veronese subalgebra $R^{(k)}$ for all $k>0$.

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Sora Miyashita. 2024-07-08. A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras. https://arxiv.org/abs/2407.05629

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