Partition of complement of good ideals and Apéry sets

Abstract

Good semigroups form a class of submonoids of 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 Apéry sets of good semigroups. This generalizes to any d ≥ 2 the results of [7], which are proved in the case d = 2 and only for the standard Apéry set with respect to the smallest nonzero element. Several new results describing good semigroups in N d are also provided.