The Arithmetic and the Geometry of Kobayashi Hyperbolicity
نویسنده
چکیده
(1) The dimension of the pluricanonical series, h(C,mK), grows linearly with m for curves of genus at least two. (2) The canonical/cotangent bundle of a curve of genus at least two is ample. (3) A curve of genus at least two admits a hyperbolic metric with constant negative curvature. (4) Curves of genus at least two are uniformized by the unit disc, hence they do not admit any non-constant holomorphic maps from C .
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