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Article Dans Une Revue Journal of Differential Geometry Année : 2020

DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES

Résumé

For smooth families X → S of projective algebraic curves and holomorphic line bundles L, M → X equipped with flat relative connections , we prove the existence of a canonical and functorial "intersection" connection on the Deligne pairing L, M → S. This generalizes the construction of Deligne in the case of Chern connections of hermitian structures on L and M. 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 mero-morphic connection on the hyperholomorphic line bundle over the twistor space of rank one flat connections on a Riemann surface.
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Dates et versions

hal-02365352 , version 1 (15-11-2019)

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Gerard Freixas Montplet, Richard Wentworth. DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES. Journal of Differential Geometry, 2020, 115 (3), pp.475--528. ⟨10.4310/jdg/1594260017⟩. ⟨hal-02365352⟩
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