Conductor and Value Semigroup of a Curve Singularity

Abstract

In this chapter we will relate the invariants of singularities of curves already introduced,such as “multiplicity,” “tangents,” “singularity degree,” “ranches,” and “intersection multiplicity between the branches,” to the conductor and value semigroup. This will allow a more precise classification of curve singularities than was possible up to now. Also, we will be led to other formulas for calculating the genus of the function field of a curve.