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

Abstract

In this article we discuss some applications of the construction of the Ap\'ery set of a good semigroup in $\mathbb{N}^d$ given in the previous paper [Partition of the complement of good semigroup ideals and Ap\'ery sets, Communications in Algebra, 49, No. 10, 4136-4158 (2021))]. In particular we study: the duality of a symmetric and almost symmetric good semigroup, the Ap\'ery set of non-local good semigroups and the Ap\'ery set of value semigroups of plane curves.