Connexions méromorphes projectives partielles et variétés algébriques hyperboliquesMeromorphic partial projective connections and hyperbolic projective varieties

Note présentée par Jean-Pierre Demailly.
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Résumé

Nous introduisons la notion de connexion projective partielle à coefficients méromorphes, et montrons comment de telles connexions peuvent servir à construire des opérateurs wronskiens globaux agissant sur les jets de courbes holomorphes. Grâce à un théorème d'annulation du wronskien reposant sur des hypothèses de négativité de la courbure de Ricci et généralisant des résultats antérieurs de Green-Griffiths, Siu et Nadel, nous donnons des exemples explicites de surfaces algébriques hyperboliques dans ℂℙ3, de degré quelconque ≥ 11.

Abstract

We introduce a concept of partial projective connection with meromorphic coefficients, and show how such connections can be used to construct global Wronskian operators acting on jets of holomorphic curves. Thanks to a vanishing theorem for Wronskian operators, relying on negativity hypotheses for the Ricci curvature, and generalizing prior results of Green-Griffiths, Siu and Nadel, we give explicit examples of hyperbolic algebraic surfaces in ℂℙ3 with arbitrary degree ≥ 11.

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