On a stability theorem for local uniformization in characteristic p (Q1110590)

The author studies the behaviour under monoidal transformations of a singular point locally expressed by the following equation: \[ z^{p^ e}+(\prod^{n}_{i=1}x_ i^{m_ i})F(x_ 1,...,x_ n)=0, \] where k is a field of characteristic p and \(F\in k[[ x_ 1,...,x_ n]]\). In particular he proves that ord(F) is stable under a sequence of permissible blow-ups.