The canonical modifications by weighted blow-ups

Details The canonical modifications by weighted blow-ups The canonical modifications by weighted blow-ups

1996-01-18

arxiv.org/abs/alg-geom/9601017v2

Mathematics

Algebraic Geometry

AMSLaTeX, 16 pages

Scientific paper

In this paper we give a criterion for an isolated, hypersurface singularity of dimension $n\ (\geq 2)$ 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 $(X,x)\subset ({\bC}^4, 0)$ and a weight ${\bw}=(w_0,w_1,\ldots ,w_n)$, such that the ${\bw}$-blow-up gives the canonical modification of $(X,x)$.

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