An approach to plane algebroid branches
  Our aim is to reprove the basic results of the theory of branches of plane algebraic curves over algebraically closed fields of arbitrary characteristic. We do not use the Hamburger-Noether expansions. Our basic tool is the logarithmic distance on the set of branches satisfying the strong triangle inequality which permits to make calculations directly on the equations of branches. 
Evelia R. Garc\'ia Barroso and Arkadiusz P{\l}oski
math.AG