The Torelli spaces of punctured tori and spheres
It is obtained an explicit realization of the Torelli spaces T'(g,k) of tori and spheres with k holes as hyperbolic domains in \({\mathbb{C}}^ m\). The explicit description of the universal covering \((g=0,1)\) T(g,k)\(\to D(g,k)\) where T(g,k) means the correspondent Teichmüller space permits to copute in nearly all cases the group Aut D(g,k). Theorem: \((1)\quad T'(0,n+3)\cong D(0,m+3)=\{z\in {\mathbb{C}}^ n:z_ i\neq z_ j,\quad i\neq j,\quad z_ i\neq 0\quad for\quad all\quad i\}.\)- (2) If the torus is defined by the lattice L(1,\(\tau)\), \(\tau \in u\), Im \(\tau >0\) then \(T'(1,n+1)\cong D(1,n+1)=\{(\tau,z)\in u\times {\mathbb{C}}^ n,\quad z_ i\not\equiv z_ j(mod L(1,\tau)),\quad i\neq j\quad and\quad z_ i\not\equiv 0(mod L(1,\tau))\quad for\quad all\quad i\}.\)
scientific article; zbMATH DE number 3867716