Accéder directement au contenu Accéder directement à la navigation
Pré-publication, Document de travail

Numerically nonspecial varieties

Abstract : Campana introduced the class of special varieties as the varieties admitting no Bogomolov sheaves i.e. rank one coherent subsheaves of maximal Kodaira dimension in some exterior power of the cotangent bundle. Campana raised the question if one can replace the Kodaira dimension by the numerical dimension in this characterization. We answer partially this question showing that a projective manifold admitting a rank one coherent subsheaf of the cotangent bundle with numerical dimension 1 is not special. We also establish the analytic characterization with the non-existence of Zariski dense entire curve and the arithmetic version with non-potential density in the (split) function field setting. Finally, we conclude with a few comments for higher codimensional foliations which may provide some evidence towards a generalization of the aforementioned results.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-03268034
Contributeur : Erwan Rousseau <>
Soumis le : mardi 22 juin 2021 - 22:23:09
Dernière modification le : jeudi 24 juin 2021 - 03:39:36

Fichiers

nonspecialv3.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-03268034, version 1
  • ARXIV : 2106.12275

Citation

Jorge Vitorio Pereira, Erwan Rousseau, Frédéric Touzet. Numerically nonspecial varieties. 2021. ⟨hal-03268034⟩

Partager

Métriques

Consultations de la notice

40

Téléchargements de fichiers

11