We describe the canonical module of a simplicial affine semigroup ring K[S] and its trace ideal. As a consequence, we characterize when 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 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.
On nearly Gorenstein affine semigroups
Strazzanti, Francesco;
2026-01-01
Abstract
We describe the canonical module of a simplicial affine semigroup ring K[S] and its trace ideal. As a consequence, we characterize when 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 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.File in questo prodotto:
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