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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local properties of quotient analytic spaces


Authors: Kunio Takijima and Tadashi Tomaru
Journal: Proc. Amer. Math. Soc. 72 (1978), 461-467
MSC: Primary 32C40; Secondary 32G11
MathSciNet review: 509235
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Abstract: Let $ T: = {\mathbf{C}}/{\mathbf{Z}}{\omega _1} + {\mathbf{Z}}{\omega _2}$ be a complex 1-torus and $ {E_n}$ the set of all elliptic functions of order n. Then M. Namba showed that $ {E_n}$ is a 2n-dimensional complex manifold. Let $ \operatorname{Aut} T$ be the automorphism group of T, then $ \operatorname{Aut} T$ is a 1-dimensional compact complex Lie group and the orbit space $ {E_n}/{\operatorname{Aut}} T$ is an analytic space. In this paper, we shall show that $ {E_n}/{\operatorname{Aut}} T$ has only rational singularities and if $ n \geqslant 5,{E_n}/{\operatorname{Aut}} T$ is rigid.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0509235-9
PII: S 0002-9939(1978)0509235-9
Keywords: Quotient analytic space, rational singularity, rigid singularity, elliptic function
Article copyright: © Copyright 1978 American Mathematical Society