Divisorial contractions to 3-dimensional terminal singularities with discrepancy one

Abstract

We study a divisorial contraction $\pi :Y\to X$ such that $\pi$ contracts an irreducible divisor $E$ to a point $P$ and that the discrepancy of $E$ is $1$ when $P\in X$ is a $3$-dimensional terminal singularity of type (cD/2) and (cE/2).