The Apéry Set of a Good Semigroup

Abstract

We study the Apéry set of good subsemigoups of ${\mathbb{N}}^2$, a class of semigroups containing the value semigroups of curve singularities with two branches. Even if this set in infinite, we show that, for the Apéry set of such semigroups, we can define a partition in "levels" that allows to generalize many properties of the Apéry set of numerical semigroups, i.e. value semigroups of one-branch singularities.

24 pages, 6 figures