On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane

We introduce the notion of curve associated with a chain of blow-ups of a complex surface. On the basis of this notion, we classify elementary chains (of length up to seven) of blow-ups of the projective plane. We prove (under an additional condition) that the ramification curve of the inverse of a polynomial mapping cannot be isolated in 4 or 5 blow-ups.