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Logarithmic jet bundles and applications. (English) Zbl 0982.32022
This paper is devoted to the understanding of the algebro-geometric and the differential-geometric meaning of hyperbolicity for complex manifolds. The authors generalize Demaille’s construction of projective jet bundles and strictly curved pseudometric on it to the logarithmic case. They introduce explicit coordinates which they hope should be a powerful tool, but they give also an intrinsic construction. They prove the Ahlfors Lemma and the Big Picard Theorem for logarithmic projective bundles. They use their method to give a metric proof of Lang’s Conjecture for semiabelian varieties and of a Big Picard analogue of it.

32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
32H25 Picard-type theorems and generalizations for several complex variables
32L05 Holomorphic bundles and generalizations
32M10 Homogeneous complex manifolds
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