2015/07/10 by Gerard Freixas i Montplet, Montplet, Gerard Freixas i, Richard Wentworth +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:14C40 #msc:58J52
paper · pdf · doi:10.48550/arxiv.1507.02920
48 pp. 1 figure
arxiv created 2015/07/10 · arxiv updated 2015/07/13
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, we prove the existence of a canonical and functorial "intersection" connection on the Deligne pairing. A relationship is found with the holomorphic extension of analytic torsion, and in the case of trivial fibrations we show that the Deligne isomorphism is flat with respect to the connections we construct. Finally, we give an application to the construction of a meromorphic connection on the hyperholomorphic line bundle over the twistor space of rank one flat connections on a Riemann surface.