A simplified proof of the Granja-Merle factorization theorem

Abstract

En [6] Granja provó una generalización del teorema de Merle [7] para curvas polares de ramas planas. El trabajo presenta una prueba de este resultado sin recurrir a la expansion de Hamburger-Noether o secuencias de Apéry (presentes en la prueba original), sino basándonos en el método desarrollado en [4].In [G] Granja proved a factorization theorem for power series in two variables which generalized the Merle theorem [M] on polar curves. Our aim is to reprove his result without resorting to Hamburger-Noether expansions and Apéry sequences. We base our proof on the method developed by us in [GB-P l].