Abstract
In this paper it is proved that the complement in ℙ2 of a holomorphic curve D of genus g≧2 is a hermitian hyperbolic complex manifold provided that certain conditions on the singularities of the dual D* of D are satisfied and that every tangent at D* intersects D* in at least two distinct points.
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Dedicated to Karl Stein
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Grauert, H., Peternell, U. Hyperbolicity of the complement of plane curves. Manuscripta Math 50, 429–441 (1985). https://doi.org/10.1007/BF01168839
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DOI: https://doi.org/10.1007/BF01168839