| Characterization of isolated homogeneous hypersurface singularities in C~4 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| 作者姓名： | YAU Stephen S T |
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| 作者单位： | Department of |
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| 摘 要： | Let V be a hypersurface with an isolated singularity at the origin in Cn 1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero.
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Characterization of isolated homogeneous hypersurface singularities in C~4 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| YAU Stephen S T.Characterization of isolated homogeneous hypersurface singularities in C~4 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday[J].Science in China(Mathematics),2006(11). |
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| Authors: | LIN Kepao TU Zhenhan & YAU Stephen S T |
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| Institution: | LIN Kepao,TU Zhenhan & YAU Stephen S T Department of Information Management,Chang Gung Institute of Technology,Taiwan,China, School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China, Department of Mathematics,Statistics and Computer Science,University of Illinois at Chicago,Chicago,IL 60607-7045,USA |
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| Abstract: | Let V be a hypersurface with an isolated singularity at the origin in Cn 1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero. |
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| Keywords: | homogeneous polynomials hypersurface singularity weighted homogeneous polynomial geometric genus |
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