Three-fold divisorial contractions to singularities of higher indices

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

2003-06-03

arxiv.org/abs/math/0306065v1

Mathematics

Algebraic Geometry

55 pages

Scientific paper

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 suitable weighted blow-up; and that if otherwise then the discrepancy is $1/n$ with a few exceptions. Every such exception has an example. Some exceptions allow the discrepancy to be arbitrarily large, but any contraction in this case is described as a weighted blow-up of a singularity of type c$D/2$ embedded into a cyclic quotient of a smooth five-fold. The erratum to the previous paper [14] is attached.

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