Local properties of quotient analytic spaces

Takijima, Kunio; Tomaru, Tadashi

doi:10.1090/S0002-9939-1978-0509235-9

Local properties of quotient analytic spaces
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by Kunio Takijima and Tadashi Tomaru

Proc. Amer. Math. Soc. 72 (1978), 461-467

DOI: https://doi.org/10.1090/S0002-9939-1978-0509235-9

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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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