Characteristic exponents of plane algebroid curves

Abstract

This chapter is devoted to the study of equisingularity of irreducible algebroid plane curves over an algebraically closed field.

Here the main idea is the construction of a complete system of invariants for the equiresolution. These invariants will be called characteristic exponents. In the characteristic zero case they are computed in the usual way by means of Puiseux expansions. In positive characteristic and in successive sections, we shall compute them by using Hamburger-Noether expansions and Newton polygons, proving, when (n,p)=1, they agree with the classical characteristic exponents.

Since the equisingularity will be considered in this chapter, we begin it by giving in the first section, a short account of Zariski's theory of equisingularity for plane curves and its meaning in the case of germs of complex analytic curves.

Throughout all this chapter, the word "curve" will stand for plane curve.