ZARISKIS EQUISINGULARITY FOR FAMILIES OF PLANE-CURVES IN POSITIVE CHARACTERISTIC

In this paper we define a concept of equisingularity for families of p lane curves in any characteristic. For this, we give a natural general ization of Zariski's equisingularity in the case of plane curves over non algebraically closed fields. This new concept avoids the pathologi es in positive characteristic of Zariski's theory. We prove that Zaris ki's concept is a particular case of ours and we also see that the new one is an open condition.