Local Properties of Quotient Analytic Spaces
Copyright policy )Local Properties of Quotient Analytic Spaces
Let T := C / Z ω 1 + Z ω 2 T: = {\mathbf {C}}/{\mathbf {Z}}{\omega _1} + {\mathbf {Z}}{\omega _2} be a complex 1-torus and E n {E_n} the set of all elliptic functions of order n. Then M. Namba showed that E n {E_n} is a 2n-dimensional complex manifold. Let Aut T \operatorname {Aut} T be the automorphism group of T, then Aut T \operatorname {Aut} T is a 1-dimensional compact complex Lie group and the orbit space E n / Aut T {E_n}/{\operatorname {Aut}} T is an analytic space. In this paper, we shall show that E n / Aut T {E_n}/{\operatorname {Aut}} T has only rational singularities and if n ⩾ 5 , E n / Aut T n \geqslant 5,{E_n}/{\operatorname {Aut}} T is rigid.
Rational Singularity, Deformations of complex singularities; vanishing cycles, Resolution of Singularities, Complex singularities, Automorphism Group, Complex Lie groups, group actions on complex spaces, Rigid Singularity, Complex Torus, Deformation Complex
Rational Singularity, Deformations of complex singularities; vanishing cycles, Resolution of Singularities, Complex singularities, Automorphism Group, Complex Lie groups, group actions on complex spaces, Rigid Singularity, Complex Torus, Deformation Complex
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