On the flip theorem for locally primitive extremal rays in dimension 3 (Q1277275)

Let \(X\) be a 3-fold with only terminal singularities and let \(C\) be a locally primitive curve whose class is an extremal ray in \(X\). In this note the author gives a proof (different from the classical one due to Mori) of the existence of a ``flip'' for \(X\), based on the following steps: (1) reduction to the case of index 1 terminal singularities, (2) construction of the blowing up of the completion of \(X\) along \(C\).