Blow-ups of three-dimensional toric singularities

Abstract: The purely log terminal blow-ups of three-dimensional terminal toric singularities are described. The three-dimensional divisorial contractions $f\colon (Y,E)\to (X\ni P)$ are described provided that $\Exc f=E$ is an irreducible divisor, $(X\ni P)$ is a toric terminal singularity, $f(E)$ is a toric subvariety and $Y$ has canonical singularities.