The Ap\'ery Set of a Good Semigroup

Abstract

We study the Ap\'ery 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 Ap\'ery set of such semigroups, we can define a partition in "levels" that allows to generalize many properties of the Ap\'ery set of numerical semigroups, i.e. value semigroups of one-branch singularities.