Partition of the complement of good semigroup ideals and Apéry sets.

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 a recent paper of D'Anna, Guerrieri and Micale, 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.