Extracting non-canonical places (Q2213795)

Let \((X,B)\) be a log canonical pair and \(\mathcal{V}\) be a finite set of divisorial valuations with log discrepancy in \([0,1).\) The authors prove that there exists a projective birational morphism \(\pi:Y\to X\) so that the exceptional locus is divisorial, the exceptional divisors are \(\mathbb{Q}\)-Cartier, and they correspond to elements of \(\mathcal{V}\). They prove it inductively on \(\#\mathcal{V}.\) From this main result they deduce several consequences such as the relation between two models \(\pi:Y\to X\) in the main result, the study of deformations of log canonical singularities, among others.