Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations
Annales de l'Institut Fourier, Volume 64 (2014) no. 6, pp. 2465-2480.

Let X be a normal projective variety, and let A be an ample Cartier divisor on X. Suppose that X is not the projective space. We prove that the twisted cotangent sheaf Ω X A is generically nef with respect to the polarisation A. As an application we prove a Kobayashi-Ochiai theorem for foliations: if T X is a foliation such that deti A, then i is at most the rank of .

Soit X une variété projective normale et A un diviseur de Cartier ample sur X. Supposons que X n’est pas l’espace projectif. Nous montrons que le faisceau cotangent tordu Ω X A est génériquement nef par rapport à la polarisation A. Comme conséquence nous obtenons un théorème de Kobayashi-Ochiai pour les feuilletages  : si T X est un feuilletage tel que deti A, alors i est au plus le rang de .

DOI: 10.5802/aif.2917
Classification: 14F10, 37F75, 14M22, 14E30, 14J40
Keywords: Cotangent sheaf, foliations, Kobayashi-Ochiai theorem
Mot clés : faisceau cotangent, feuilletages, théorème de Kobayashi-Ochiai
Höring, Andreas 1

1 Laboratoire de Mathématiques J.A. Dieudonné UMR 7351 CNRS Université de Nice Sophia-Antipolis 06108 Nice Cedex 02 (France)
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Höring, Andreas. Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations. Annales de l'Institut Fourier, Volume 64 (2014) no. 6, pp. 2465-2480. doi : 10.5802/aif.2917. https://aif.centre-mersenne.org/articles/10.5802/aif.2917/

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