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

We consider the faithfulness of the monodromy representation associated with the universal family of n-pointed algebraic curves of genus g (2 - 2g - n < 0). We shall show that the restriction rho (g,n) of the representation to the geometric fundamental group is faithful for g = 0, 1. We shall also show that if rho (g,n) is faithful, then so is rho (g,n+1). (C) 2001 Elsevier Science B.V. All rights reserved.