The faithfulness of the monodromy representations associated with certain families of algebraic curves

Abstract

We consider the faithfulness of the monodromy representation associated with the universal family of n-pointed algebraic curves of genus g (2−2 g− n<0). We shall show that the restriction ρ g, n of the representation to the geometric fundamental group is faithful for g=0,1. We shall also show that if ρ g, n is faithful, then so is ρ g, n+1 .