The Torelli spaces of punctured tori and spheres
type: Item
instance of: scholarly article
title: The Torelli spaces of punctured tori and spheres
zbMATH Open document ID: 0545.32010
DOI: 10.1215/S0012-7094-81-04821-3
author: Subhashis Nag
published in: Duke Mathematical Journal
publication date: 1981-01-01T00:00:00Z
review text: 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 \(T'(1,n+1)\cong D(1,n+1)=\{(\tau,z)\in u\times {\mathbb{C}}^ n,\quad z_ i\not\equiv z_ j(mod L(1,\tau)),\quad i\neq j\quad and\quad z_ i\not\equiv 0(mod L(1,\tau))\quad for\quad all\quad i\}.\)
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 3867716
zbMATH Keywords: Torelli spaces of punctured tori
zbMATH Keywords: Torelli spaces of punctured spheres
zbMATH Keywords: Teichmüller space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3867716