Arf good semigroups

Abstract

In this thesis we explore the properties of the Arf good subsemigroups of N^r, with r>1. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of determining the Arf closure of a set of vectors and of a good semigroup, extending the concept of characters of an Arf numerical semigroup to Arf good semigroups. Furthermore we present some procedures to calculate the set of the Arf good semigroups with a given conductor and with a given genus. Finally we give an effcient algorithm for the computation of the Arf Closure of an algebroid curve with more than one branch.