Deux exemples sur la dimension moyenne d'un espace de courbes de Brody
Complex Variables
2011-10-28 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1110.6082,
title = {Deux exemples sur la dimension moyenne d'un espace de courbes de Brody},
author = {Bernardo Freitas Paulo Da Costa},
journal= {arXiv preprint arXiv:1110.6082},
year = {2011}
}
Comments
14p