## Duke Mathematical Journal

### Three-fold divisorial contractions to singularities of higher indices

Masayuki Kawakita

#### Abstract

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 $n \ge 2$. We prove that if this singularity is of type c$A/n$, then any such contraction is a weighted blowup; and that if otherwise, then $f$ is either a weighted blowup of a singularity of type c$D/2$ embedded into a cyclic quotient of a smooth five-fold, or a contraction with discrepancy $1/n$, 1, or 2. Every such exceptional case of discrepancy 1 or 2 has an example. The erratum to our previous article [13] appears in the appendix.

#### Article information

Source
Duke Math. J., Volume 130, Number 1 (2005), 57-126.

Dates
First available in Project Euclid: 12 November 2005

https://projecteuclid.org/euclid.dmj/1131804020

Digital Object Identifier
doi:10.1215/S0012-7094-05-13013-7

Mathematical Reviews number (MathSciNet)
MR2176548

Zentralblatt MATH identifier
1091.14008

#### Citation

Kawakita, Masayuki. Three-fold divisorial contractions to singularities of higher indices. Duke Math. J. 130 (2005), no. 1, 57--126. doi:10.1215/S0012-7094-05-13013-7. https://projecteuclid.org/euclid.dmj/1131804020

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