Remarks on rational points of universal curves

Abstract

In this note, we will give some remarks on the results in [J. Amer. Math. Soc. 24 (2011), no. 3, pp. 709–769] by Hain. In particular, we consider the universal curves M g , n + 1 → M g , n {\mathcal {M}}_{g,n+1}\to {\mathcal {M}}_{g,n} and the sections of their algebraic fundamental groups.