Deux exemples sur la dimension moyenne d'un espace de courbes de Brody

Details Deux exemples sur la dimension moyenne d'un espace de courbes de Brody Deux exemples sur la dimension moyenne d'un espace de courbes de Brody

2011-10-27

arxiv.org/abs/1110.6082v1

Mathematics

Complex Variables

14p

Scientific paper

We study the mean dimension of the space of 1-Brody curves lying in two complex surfaces: first for Hopf surfaces, then for the projective plane minus a line. We show in the first case that the mean dimension is zero via a bound on the growth of meromorphic curves involving the logarithmic derivative lemma. In the second case, we show its positivity by lifting from the line to its complement a space of Brody curves of positive mean dimension containing deformations of an elliptic curve.

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