Properties and applications of the Apéry set of good semigroups in $$\mathbb {N}^d$$

Abstract In this article, we discuss some applications of the construction of the Apéry set of a good semigroup in $$\mathbb {N}^d$$ N d given in (Commun Algebra 49(10):4136–4158, 2021). In particular, we study the duality of a symmetric and almost symmetric good semigroup, the Apéry set of non-local good semigroups and the Apéry set of value semigroups of plane curves.