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 [Col02] where she constructed the extension corresponding to Collino's cycles in the Jacobian of a hyperelliptic curve.
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