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).
@article{1158241927,
author = {HAYAKAWA, Takayuki},
title = {Divisorial contractions to 3-dimensional terminal singularities with discrepancy one},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 651-668},
language = {en},
url = {http://dml.mathdoc.fr/item/1158241927}
}
HAYAKAWA, Takayuki. Divisorial contractions to 3-dimensional terminal singularities with discrepancy one. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 651-668. http://gdmltest.u-ga.fr/item/1158241927/