Where can I find an elementary introduction (construction, description, main properties) to the Teichmüller space ${\cal T}_{1,n}$ of elliptic curves with $n$-marked points?

Same question for the following associated objects: mapping class group $\Gamma_{1,n}$ and moduli space ${\cal M}_{1,n}={\cal T}_{1,n}/\Gamma_{1,n}$.

Thanks in advance for any reference.

  • $\begingroup$ It is the same in genus 1 as for the arbitrary genus. Any book with words 'Teichmuller theory' in the title would work. $\endgroup$ – Misha Oct 8 '13 at 14:03
  • $\begingroup$ Because elliptic curves have explicit uniformizations, I was expecting that ${\cal T}_{1,n}$ can be described quite concretely... $\endgroup$ – Elbabak Oct 8 '13 at 14:16
  • 1
    $\begingroup$ Elliptic curves yes, but not the ones with punctures. $\endgroup$ – Misha Oct 8 '13 at 18:23
  • $\begingroup$ A recent related question: mathoverflow.net/questions/162690/… $\endgroup$ – Lee Mosher Apr 13 '14 at 13:23

On these questions, the following reference could be helpful:

S. NAG, The torelli spaces of punctured tori and spheres Duke Math. Journal 48 (1981), p. 359-388.



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