1996/01/18 by Shihoko Ishii, Ishii, Shihoko
Mathematics · #14 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #alg-geom #math.AG #msc:14
paper · pdf · doi:10.48550/arxiv.alg-geom/9601017
AMSLaTeX, 16 pages
arxiv created 1996/01/18 · openalex publication_date 1996/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give a criterion for an isolated, hypersurface singularity of dimension n (≥ 2) to have the canonical modification by means of a suitable weighted blow-up. Then we give a counter example to the following conjecture by Reid-Watanabe: For a 3-dimensional, isolated, non-canonical, log-canonical singularity (X,x) of embedded dimension 4, there exists an embedding (X,x)⊂ (\bC4, 0) and a weight \bw=(w0,w1,… ,wn), such that the \bw-blow-up gives the canonical modification of (X,x).