Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Höring, Andreas

doi:10.5802/aif.2917

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations [ Faisceaux cotangents tordus et un théorème de Kobayashi-Ochiai pour les feuilletages ]

Höring, Andreas

Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2465-2480.

Résumé
Abstract

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 $Ω_{X} \otimes A$ est génériquement nef par rapport à la polarisation $A$ . Comme conséquence nous obtenons un théorème de Kobayashi-Ochiai pour les feuilletages : si $ℱ ⊊ T_{X}$ est un feuilletage tel que $det ℱ \equiv i_{ℱ} A$ , alors $i_{ℱ}$ est au plus le rang de $ℱ$ .

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 $Ω_{X} \otimes A$ is generically nef with respect to the polarisation $A$ . As an application we prove a Kobayashi-Ochiai theorem for foliations: if $ℱ ⊊ T_{X}$ is a foliation such that $det ℱ \equiv i_{ℱ} A$ , then $i_{ℱ}$ is at most the rank of $ℱ$ .

Reçu le : 2013-07-23
Révisé le : 2014-05-16
Accepté le : 2014-06-13

MR 3331171 | Zbl 06387344

DOI : https://doi.org/10.5802/aif.2917
Classification : 14F10, 37F75, 14M22, 14E30, 14J40
Mots clés : faisceau cotangent, feuilletages, théorème de Kobayashi-Ochiai

@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'institut Fourier},
     volume = {64},
     number = {6},
     year = {2014},
     doi = {10.5802/aif.2917},
     zbl = {06387344},
     mrnumber = {3331171},
     language = {en},
     url = {https://aif.centre-mersenne.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, Tome 64 (2014) no. 6, pp. 2465-2480. doi : 10.5802/aif.2917. https://aif.centre-mersenne.org/item/AIF_2014__64_6_2465_0/

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