Statement: the group of complex automorphisms of the moduli space $M_{0,n}$ of complex $n$-marked genus 0 curves is isomorphic to $\mathfrak S_n$: one has ${\rm Aut}(M_{0,n})=\mathfrak S_n$
I believe that this is true for $n\geq 5$ (what about the cases $n=3,4$?) and has been obtained in the 50's by peoples working in Teichmuller theory.
Questions:
- Is this statement correct ?
- If it is, who has to be credited for it?
Classical/canonical references as well as recent but very useful/relevant references are welcome !
Thanks in advance
Remark: if $\overline{M}_{0,n}$ stands for Deligne-Mumford-Knudsen moduli space of stable $n$-marked genus 0 curves, that ${\rm Aut}(\overline{M}_{0,n})=\mathfrak S_n$ has been proved only recently (in [A. Bruno, M. Mella]: The automorphism group of $\overline{M}_{0,n}$, J. Eur. Math. Soc., Volume 15 (2013), pp. 949-968).