  We consider a resolution of ramified irregular singularities of meromorphic
connections on a formal disk via local Fourier transforms. A necessary and
sufficient condition for an irreducible connection to have a resolution of the
ramified singularity is determined as an analogy of the blowing up of plane
curve singularities. We also relate the irregularity of Komatsu and Malgrange
of connections to the intersection numbers and the Milnor numbers of plane
curve germs. Finally, we shall define an analogue of Puiseux characteristics
for connections and find an invariant of the family of connections with the
fixed Puiseux characteristic by means of the structure of iterated torus knots
of the plane curve germs.
