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 ${\mathbb{N}}^d$ given in the previous paper [Partition of the complement of good semigroup ideals and Apéry 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 Apéry set of non-local good semigroups and the Apéry set of value semigroups of plane curves.

31 pages, 7 figures