Improved Kobayashi hyperbolicity bounds: generic surfaces in P^3 of degree >=17 and curve complements in P^2 of degree >=12, via vanishing of negatively twisted invariant 2-jet differentials.
The complement to a general hypersurface of degree2ninCP n is not hyperbolic.Sibirsk
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Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two
Improved Kobayashi hyperbolicity bounds: generic surfaces in P^3 of degree >=17 and curve complements in P^2 of degree >=12, via vanishing of negatively twisted invariant 2-jet differentials.