Abstract: An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces X in ℙn: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of X, and the Kobayashi Conjecture, which says that X contains no entire curves.
We prove that (a slightly strengthened version of) the Green-Griffiths-Lang Conjecture in dimension 2n implies the Kobayashi Conjecture in dimension n. The technique has already led to improved bounds for the Kobayashi Conjecture. This is joint work with David Yang.
Recording during the meeting "Entire Curves, Rational Curves and Foliations" the February 18, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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