The fundamental group and extensions of motives of Jacobians of curves

In this paper, we construct extensions of mixed Hodge structure coming from the mixed Hodge structure on the graded quotients of the group ring of the fundamental group of a smooth projective pointed curve which correspond to the regulators of certain motivic cohomology cycles on the Jacobian of the curve essentially constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. This is a generalisation of a theorem of Colombo (J. Algebr. Geom.11(4) (2002) 761-790) where she constructed the extension corresponding to Collino's cycles in the Jacobian of a hyperelliptic curve.