TOPOLOGICAL CLASSIFICATION OF IRREDUCIBLE PLANE CURVE SINGULARITIES IN TERMS OF WEIERSTRASS POLYNOMIALS

Let f(z, y) be analytically irreducible at 0 and f(0) = 0. Then the plane curve singularity defined by f has the same topological type as the curve defined by f(k+1) for some k greater than or equal to 0 where f(1) = z(a) + y(b), f(2) = f(1)(n21) + y(m11)z(m12), f(3) = f(2)(n31) + f(1)(n22)y(m21)z(m22), ... are defined by induction on k with distinct numerical conditions topologically invariant. Moreover, we give an easy alternate proof of Zariski's topological classification theorem of irreducible plane curve singularities.