A remark on the automorphisms of the moduli space \({\mathcal M} _ g\) of compact Riemann surfaces (Q811651)

Based on facts on automorphism groups generated by generalized reflections a short proof of the following theorem of Rauch is given: The canonical map from the Teichmüller space of Riemann surfaces of genus larger than three to the moduli space is nowhere branched in codimension one. Now Royden's theorem implies that the automorphism group of the moduli space \({\mathcal M}_ g\) is trivial for \(g>3\) which does not hold for \(g=2\).