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Title:
Deligne Pairings and Flat Connections
Speaker:
Abstract:
On a smooth holomorphic fibration of projective curves the Deligne pairing produces a line bundle on the base parameter space from a pair of line bundles on the total space of the family. If the line bundles are endowed with metrics then the pairing has a canonically defined metric as well. I will introduce a generalization of this construction where metrics are replaced by relatively flat connections. This gives an interpretation via the Deligne isomorphism of the holomorphic extension of analytic torsion on considered by Fay and Cappell-Miller. The hyperholomorphic line bundle on the twistor space of the moduli of Higgs bundles admits a meromorphic connection with certain properties. I will show that the existence of this connection for rank one Higgs bundles also follows naturally from our construction. This is joint work with Gerard Freixas I Montplet.
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