2003/06/03 by Masayuki Kawakita, Kawakita, Masayuki · 1 citation
Mathematics · #14E05 #14E30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14E05 #msc:14E30
paper · pdf · doi:10.48550/arxiv.math/0306065
55 pages
arxiv created 2003/06/03 · openalex publication_date 2003/06/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≥ 2. We prove that if this singularity is of type cA/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 cD/2 embedded into a cyclic quotient of a smooth five-fold. The erratum to the previous paper [14] is attached.