Approximate roots
by
Patrick Popescu-Pampu
Ecole Normale Superieure, Paris

Approximate roots are defined for polynomials over arbitrary commutative rings. In this talk we shall present properties of them for irreducible polynomials in C[[x]][y]. They were introduced by Abhyankar and Moh to deal with global problems in the plane; here we will focus only on local aspects: their intersections with {f=0} generate the semigroup of this curve and they are locally irreducible. Moreover, we shall interpret these informations in terms of the strict transforms of the approximate roots in the minimal embedded resolution of {f=0}.

Date received: July 5, 1999