Combinatorial analysis of point obstructions to local factorizability in three-folds

Abstract

The paper introduces formally the concept of local factorizability used in earlier factorizability work, identifies the basic form of obstructions to local factorizability of birational morphisms, and outlines a combinatorial technique for analyzing such obstructions. As an application and illustration, two open cases in the classification of birational morphisms with small canonical divisors are settled.