The semigroup of a space curve singularity

Abstract

The semigroup of values of a space curve singularity is an invariant of the singularity. We analyze the complexity of this invariant, in order to describe the geometric invariants of the sequence of infinitely near points of the curve necessary to determine the generators of the semigroup. We give several approaches and examples using Hamburger–Noether matrices to describe the infinitely near points of the curve.