Let (X,B) be a log canonical pair and V be a finite set of divisorial valuations with log discrepancy in [0,1). We prove that there exists a projective birational morphism π:Y→X so that the exceptional locus is divisorial, the exceptional divisors are Q-Cartier, and they correspond to elements of V. We study how two such models are related. As applications, we apply the main theorem to the study of deformations of log canonical singularities. Furthermore, we prove the existence of rationalization for log canonical singularities.
All Science Journal Classification (ASJC) codes
- Minimal model program
- lc places
- lc singularities