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

Bernardo Freitas Paulo da Costa (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: mean dimension; Brody curves; Hopf surfaces; divisor complement

Domaines: Variables complexes [math.CV]

Bernardo Freitas Paulo da Costa. Deux exemples sur la dimension moyenne d'un espace de courbes de Brody. 2011. ⟨hal-00636504⟩