Almost Gorenstein homogeneous rings and their $h$-vectors

Akihiro Higashitani

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arXiv · 1507.03307

Almost Gorenstein homogeneous rings and their $h$-vectors

Akihiro Higashitani

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Abstract

In this paper, for the development of the study of almost Gorenstein graded rings, we discuss some relations between almost Gorensteinness of Cohen--Macaulay homogeneous rings and their $h$-vectors. Concretely, for a Cohen--Macaulay homogeneous ring $R$, we give a sufficient condition for $R$ to be almost Gorenstein in terms of the $h$-vector of $R$ and we also characterize almost Gorenstein homogeneous domains with small socle degrees in terms of the $h$-vector of $R$. Moreover, we also provide the examples of almost Gorenstein homogeneous domains arising from lattice polytopes.

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Akihiro Higashitani. 2015-07-13. Almost Gorenstein homogeneous rings and their $h$-vectors. https://arxiv.org/abs/1507.03307

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