We complete the explicit study of a three-fold divisorial contraction whose exceptional divisor contracts to a point by treating the case where the point downstairs is a singularity of index . We prove that if this singularity is of type c, then any such contraction is a weighted blowup; and that if otherwise, then is either a weighted blowup of a singularity of type c embedded into a cyclic quotient of a smooth five-fold, or a contraction with discrepancy , 1, or 2. Every such exceptional case of discrepancy 1 or 2 has an example. The erratum to our previous article  appears in the appendix.
Masayuki Kawakita. "Three-fold divisorial contractions to singularities of higher indices." Duke Math. J. 130 (1) 57 - 126, 01 October 2005. https://doi.org/10.1215/S0012-7094-05-13013-7