On the Parameterization of Germs of Two-Dimensional Singularities

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• 作者：Mihnea Col?oiu ; Cezar Joi?a
• 关键词：Two ; dimensional singularity ; Quotient singularity ; Proper modifications ; 32B10 ; 32B30 ; 32C45
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：25
• 期：4
• 页码：2427-2435
• 全文大小：395 KB
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• 作者单位：Mihnea Col?oiu (1)
  Cezar Joi?a (1)
  
  1. Institute of Mathematics of the Romanian Academy, Research Unit 3, P.O. Box 1-764, 014700?, Bucharest, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

We consider a germ of a two-dimensional complex singularity \((X,x_0)\), irreducible at \(x_0\) and \(F\) the exceptional divisor of a desingularization. We prove that if there exists a normal isolated singularity \((Z,z_0)\) with simply connected link and a surjective holomorphic map \(f:(Z,z_0)\rightarrow (X,x_0)\) then all irreducible components of \(F\) are rational, and if all irreducible components of \(F\) are rational then there exists a surjective holomorphic map \(f:(\mathbb {C}^2,0)\rightarrow (X,x_0)\). Keywords Two-dimensional singularity Quotient singularity Proper modifications