Partition of the complement of good semigroup ideals and Apéry sets. Issue 10 (4th August 2021) - Guerrieri, L.; Maugeri, N.; Micale, V.
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 complement of good semigroup ideals. As main application, we describe the Apéry sets of good semigroups with respect to arbitrary elements. This generalizes to any d ≥ 2 the results in the study of D'Anna et al., 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.