Quasihomogeneous singularities
type: Item
instance of: scholarly article
title: Quasihomogeneous singularities
zbMATH Open document ID: 0625.14019
DOI: 10.1007/BF01458435
author: Bernhard Runge
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164420
review text: If one has an ample line bundle over a projective variety \(X\) with a group action, one may contract the zero section and then divide the cone by the group-action. These varieties are called cone quotients of \(X\). \textit{Pinkham} showed that analytically every quasihomogeneous normal surface singularity is a cone quotient of a curve and that the resolution graph is star-shaped. This holds also algebraically for any characteristic and the group may be chosen abelian. One gets a bijection between quasihomogeneous normal surface singularities and the data of the resolution in the algebraic category.
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 4014889
zbMATH Keywords: quasihomogeneous normal surface singularity
zbMATH Keywords: resolution graph
MaRDI profile type: Publication
cites work: On resolutions of cyclic quotient singularities
cites work: Q772397
cites work: On G-linebundles and \(K_ G^{\bullet}(X)\)
cites work: Q4192182
cites work: Normal surface singularities with \(\mathbb{C}^*\) action
OpenAlex ID: W3187556554
description: scientific article; zbMATH DE number 4014889