turkmath.org

I will first describe the structure of the local ring of a singular branch and explain how the blow up process affects it. Then I will describe, aprés Arf, how the multiplicity sequence can be recovered, not from this ring but from a slightly larger and nicer ring which is now known as the Arf ring. The process of finding this nicer ring is known as the Arf closure of this ring. Finally I will explain how Arf answered Du Val's question of reading off the multiplicity sequence from the local ring. Arf's original article "Une interpretation algebrique de la suite des ordres de multiplicite d'une branche algebrique", together with my English translation can be found on: http://sertoz.bilkent.edu.tr/arf.htm