Decompositions of the higher order polars of plane branches
  \noindent In \cite{Casas} Casas-Alvero found decompositions of higher order polars of an irreducible plane curve generalizing the results of Merle. We improve his result giving a finer decomposition where we determine the topological type and the number of a kind of branches that we call {\em threshold semi-roots}. 
Evelia R. Garc\'ia Barroso and Janusz Gwo\'zdziewicz
math.AG