Duke Mathematical Journal

Three-fold divisorial contractions to singularities of higher indices

Masayuki Kawakita

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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 n2. We prove that if this singularity is of type cA/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 cD/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.

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

First available in Project Euclid: 12 November 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E05: Rational and birational maps 14E30: Minimal model program (Mori theory, extremal rays)


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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