Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations
Annales de l'Institut Fourier, Volume 64 (2014) no. 6, p. 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 : https://doi.org/10.5802/aif.2917
Classification:  14F10,  37F75,  14M22,  14E30,  14J40
Keywords: Cotangent sheaf, foliations, Kobayashi-Ochiai theorem
@article{AIF_2014__64_6_2465_0,
     author = {H\"oring, Andreas},
     title = {Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {6},
     year = {2014},
     pages = {2465-2480},
     doi = {10.5802/aif.2917},
     mrnumber = {3331171},
     zbl = {06387344},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_6_2465_0}
}
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. http://www.numdam.org/item/AIF_2014__64_6_2465_0/

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