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For smooth families of projective algebraic curves, we extend the notion ofintersection pairing of metrized line bundles to a pairing on line bundles withflat relative connections. In this setting, we prove the existence of acanonical and functorial "intersection" connection on the Deligne pairing. Arelationship is found with the holomorphic extension of analytic torsion, andin the case of trivial fibrations we show that the Deligne isomorphism is flatwith respect to the connections we construct. Finally, we give an applicationto the construction of a meromorphic connection on the hyperholomorphic linebundle over the twistor space of rank one flat connections on a Riemannsurface.

Deligne pairings and families of rank one local systems on algebraic curves