Let be a normal projective variety, and let be an ample Cartier divisor on . Suppose that is not the projective space. We prove that the twisted cotangent sheaf is generically nef with respect to the polarisation . As an application we prove a Kobayashi-Ochiai theorem for foliations: if is a foliation such that , then is at most the rank of .
Soit une variété projective normale et un diviseur de Cartier ample sur . Supposons que n’est pas l’espace projectif. Nous montrons que le faisceau cotangent tordu est génériquement nef par rapport à la polarisation . Comme conséquence nous obtenons un théorème de Kobayashi-Ochiai pour les feuilletages : si est un feuilletage tel que , alors est au plus le rang de .
Keywords: Cotangent sheaf, foliations, Kobayashi-Ochiai theorem
Mot clés : faisceau cotangent, feuilletages, théorème de Kobayashi-Ochiai
Höring, Andreas 1
@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}, pages = {2465--2480}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {6}, year = {2014}, doi = {10.5802/aif.2917}, mrnumber = {3331171}, zbl = {06387344}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2917/} }
TY - JOUR AU - Höring, Andreas TI - Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations JO - Annales de l'Institut Fourier PY - 2014 SP - 2465 EP - 2480 VL - 64 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2917/ DO - 10.5802/aif.2917 LA - en ID - AIF_2014__64_6_2465_0 ER -
%0 Journal Article %A Höring, Andreas %T Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations %J Annales de l'Institut Fourier %D 2014 %P 2465-2480 %V 64 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2917/ %R 10.5802/aif.2917 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2917/
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