Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring[1]

  • [1] Laboratoire de Mathématiques J.A. Dieudonné UMR 7351 CNRS Université de Nice Sophia-Antipolis 06108 Nice Cedex 02 (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 6, page 2465-2480
  • ISSN: 0373-0956

Abstract

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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 ℱ ⊊ T X is a foliation such that det ℱ ≡ i ℱ A , then i ℱ is at most the rank of ℱ .

How to cite

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Höring, Andreas. "Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations." Annales de l’institut Fourier 64.6 (2014): 2465-2480. <http://eudml.org/doc/275630>.

@article{Höring2014,
abstract = {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 $\Omega _X \otimes A$ is generically nef with respect to the polarisation $A$. As an application we prove a Kobayashi-Ochiai theorem for foliations: if $\mathcal\{F\} \subsetneq T_X$ is a foliation such that $\det \mathcal\{F\} \equiv i_\{\mathcal\{F\}\} A$, then $i_\{\mathcal\{F\}\}$ is at most the rank of $\mathcal\{F\}$.},
affiliation = {Laboratoire de Mathématiques J.A. Dieudonné UMR 7351 CNRS Université de Nice Sophia-Antipolis 06108 Nice Cedex 02 (France)},
author = {Höring, Andreas},
journal = {Annales de l’institut Fourier},
keywords = {Cotangent sheaf; foliations; Kobayashi-Ochiai theorem; cotangent sheaf},
language = {eng},
number = {6},
pages = {2465-2480},
publisher = {Association des Annales de l’institut Fourier},
title = {Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations},
url = {http://eudml.org/doc/275630},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Höring, Andreas
TI - Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 6
SP - 2465
EP - 2480
AB - 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 $\Omega _X \otimes A$ is generically nef with respect to the polarisation $A$. As an application we prove a Kobayashi-Ochiai theorem for foliations: if $\mathcal{F} \subsetneq T_X$ is a foliation such that $\det \mathcal{F} \equiv i_{\mathcal{F}} A$, then $i_{\mathcal{F}}$ is at most the rank of $\mathcal{F}$.
LA - eng
KW - Cotangent sheaf; foliations; Kobayashi-Ochiai theorem; cotangent sheaf
UR - http://eudml.org/doc/275630
ER -

References

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