Criteria for the canonicity of cyclic quotients of regular and nondegenerate double singular points
type: Item
instance of: scholarly article
title: Criteria for the canonicity of cyclic quotients of regular and nondegenerate double singular points
zbMATH Open document ID: 0633.14002
DOI: 10.1007/BF00971300
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let k be an algebraically closed field with \(char(k)=0\), \(\mu_ r\) the cyclic group of \(r^{th}\) roots of unity, \(a_ 1, a_ 2, a_ 3\) integers such that \(0<a_ i<r\), \((a_ i,r)=1\). Then the factor variety \(A^ 3/\mu_ r\) given by the action \((x_ 1,x_ 2,x_ 3)\to (\epsilon^{a_ 1}x_ 1,\epsilon^{a_ 2}x_ 2,\epsilon^{a_ 3}x_ 3)\), \(\epsilon \in \mu_ r\) is a canonical singularity iff for every \(t\in {\mathbb{Z}}\), \(1\leq t\leq r-1\), it holds \(\{ta_ 1/r\}+\{ta_ 2/r\}+\{ta_ 3/r\}\geq 1\), where \(\{\) \(b\}\) denotes the fractional part of a rational number b. Finally the author studies canonical factors of quadratic singularities.
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 4029723
zbMATH Keywords: factor variety
zbMATH Keywords: canonical singularity
zbMATH Keywords: quadratic singularities
author: Sergei Konyagin
author: D. Markushevich
MaRDI profile type: Publication
cites work: Threefolds whose canonical bundles are not numerically effective
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cites work: Toroidal embeddings. I
cites work: Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
full work available at URL: https://doi.org/10.1007/bf00971300
OpenAlex ID: W2014849795
description: scientific article; zbMATH DE number 4029723