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arXiv · 2005.12354

Partition of complement of good ideals and Ap\'{e}ry sets

Lorenzo Guerrieri·Nicola Maugeri·Vincenzo Micale
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Abstract

Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the description of the Ap\'{e}ry sets of good semigroups. This generalizes to any $d \geq 2$ the results of a recent paper of D'Anna, Guerrieri and Micale, which are proved in the case $d=2$ and only for the standard Ap\'{e}ry set with respect to the smallest nonzero element. Several new results describing good semigroups in $\mathbb{N}^d$ are also provided.

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Lorenzo Guerrieri, Nicola Maugeri, Vincenzo Micale. 2020-05-25. Partition of complement of good ideals and Ap\'{e}ry sets. https://arxiv.org/abs/2005.12354

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