On the logarithmic Kobayashi conjecture
| dc.creator | Pacienza, Gianluca | |
| dc.creator | Rousseau, Erwan | |
| dc.date | 2006-03-30 | |
| dc.date.accessioned | 2026-07-07T07:07:23Z | |
| dc.date.available | 2026-07-07T07:07:23Z | |
| dc.description | We study the hyperbolicity of the log variety $(\mathbb{P}^n, X)$, where $X$ is a very general hypersurface of degree $d\geq 2n+1$ (which is the bound predicted by the Kobayashi conjecture). Using a positivity result for the sheaf of (twisted) logarithmic vector fields, which may be of independent interest, we show that any log-subvariety of $(\mathbb{P}^n, X)$ is of log-general type, give a new proof of the algebraic hyperbolicity of $(\mathbb{P}^n, X)$, and exclude the existence of maximal rank families of entire curves in the complement of the universal degree $d$ hypersurface. Moreover, we prove that, as in the compact case, the algebraic hyperbolicity of a log-variety is a necessary condition for the metric one. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603712 | |
| dc.identifier | http://arxiv.org/abs/math/0603712 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110370 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J70; 32Q45 | |
| dc.title | On the logarithmic Kobayashi conjecture | |
| dc.type | text |