标题： 有限补集单纯仿射半群的Buchsbaum性质 显示英文标题

标题： Buchsbaumness of finite complement simplicial affine semigroups

摘要： 在本文中，我们分类了所有在其（整数）有理多面体锥体补集为有限的Buchsbaum单纯仿射半群。我们证明，这样的半群是Buchsbaum当且仅当其间隙集合等于其伪Frobenius元素集合。此外，我们提供了这些仿射半群的完整结构。在嵌入维数最大的仿射半群情况下，我们提供了一个显式公式，用于计算最小表示的基数，该公式涉及极射线的数量、嵌入维数和亏格。最后，我们观察到，与完备交截、Cohen-Macaulay和Gorenstein性质不同，Buchsbaum性质在仿射半群的粘合下不保持。 显示英文摘要

摘要： In this article, we classify all Buchsbaum simplicial affine semigroups whose complement in their (integer) rational polyhedral cone is finite. We show that such a semigroup is Buchsbaum if and only if its set of gaps is equal to its set of pseudo-Frobenius elements. Furthermore, we provide a complete structure of these affine semigroups. In the case of affine semigroups with maximal embedding dimension, we provide an explicit formula for the cardinality of the minimal presentation in terms of the number of extremal rays, the embedding dimension, and the genus. Finally, we observe that, unlike the complete intersection, Cohen-Macaulay, and Gorenstein properties, the Buchsbaum property is not preserved under gluing of affine semigroups.