Comptes Rendus
no. 9
Algebraic geometry/Analytic geometry
Kobayashi measure hyperbolicity for singular directed varieties of general type
Jean-Pierre Demailly
Ya Deng1, 2
1Institut Fourier, Université Grenoble Alpes, France
2School of Mathematical Sciences, University of Science and Technology of China, China
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 920-924

In this note, we prove the non-degeneracy of the Kobayashi–Eisenman volume measure of a singular directed varieties (X,V), i.e. the Kobayashi measure hyperbolicity of (X,V), as long as the canonical sheaf KV of V is big in the sense of Demailly.

Dans cette note, nous démontrons la non-dégénérescence de la mesure de volume au sens de Kobayashi–Eisenman pour une variété dirigée singulière (X,V), c'est-à-dire l'hyperbolicité de la mesure au sens de Kobayashi de (X,V) lorsque le faisceau canonique KV de V est gros au sens de Demailly.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.07.010

Ya Deng  1 , 2

1 Institut Fourier, Université Grenoble Alpes, France
2 School of Mathematical Sciences, University of Science and Technology of China, China 
Ya Deng. Kobayashi measure hyperbolicity for singular directed varieties of general type. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 920-924. doi: 10.1016/j.crma.2016.07.010
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