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arXiv · 2411.12081

On nearly Gorenstein affine semigroups

Raheleh Jafari·Francesco Strazzanti·Santiago Zarzuela Armengou
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Abstract

We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$. Then, we find some bounds for the Cohen-Macaulay type of $\mathbb{K}[S]$ when it is nearly Gorenstein. In particular, if it has codimension at most three, we prove that the Cohen-Macaulay type is at most three and this bound is sharp.

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Raheleh Jafari, Francesco Strazzanti, Santiago Zarzuela Armengou. 2024-11-18. On nearly Gorenstein affine semigroups. https://arxiv.org/abs/2411.12081

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