Advertisement

On Foliations with Semi-positive Anti-canonical Bundle

  • Stéphane Druel
Article
  • 14 Downloads

Abstract

In this note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.

Keywords

Foliation Compact leaf Algebraically integrable foliation 

Mathematics Subject Classification

37F75 

Notes

Acknowledgements

We would like to thank Andreas Höring for useful discussions. The author was partially supported by the ALKAGE project (ERC Grant Nr 670846, 2015−2020) and the Foliage project (ANR Grant Nr ANR-16-CE40-0008-01, 2017−2020).

References

  1. Araujo, C., Druel, S.: On fano foliations. Adv. Math. 238, 70–118 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Araujo, C., Druel, S.: On codimension 1 del Pezzo foliations on varieties with mild singularities. Math. Ann. 360(3–4), 769–798 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Campana, F., Păun, M.: Foliations with positive slopes and birational stability of orbifold cotangent bundles, preprint. arXiv:1508:0245v4 (2015)
  4. Demailly, J.-P., Peternell, T., Schneider, M.: Pseudo-effective line bundles on compact Kähler manifolds. Internat. J. Math. 12(6), 689–741 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. Druel, S.: Regular foliations on weak fano manifold, Ann. Fac. Sci. Toulouse Math. (6) 26(1), 207–217 (2017a)Google Scholar
  6. Druel, S.: On foliations with nef anti-canonical bundle. Trans. A. Math. Soc. 369(11), 7765–7787 (2017b)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Druel, S.: Some remarks on regular foliations with numerically trivial canonical class, EPIGA 1 (2017c)Google Scholar
  8. Druel, S.: Codimension one foliations with numerically trivial canonical class on singular spaces, preprint arXiv:1809.06905 (2018)
  9. Druel, S.: A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Invent. Math. 211(1), 245–296 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Graber, T., Harris, J., Starr, J.: Families of rationally connected varieties. J. Am. Math. Soc. 16(1), 57–67 (2003). (electronic)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Loray, F., Pereira, J.V., Touzet, F.: Singular foliations with trivial canonical class. Invent. Math. 213(3), 1327–1380 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  12. Pereira, J.V., Touzet, F.: Foliations with vanishing Chern classes. Bull. Braz. Math. Soc. (N.S.) 44(4), 731–754 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. Touzet, F.: Feuilletages holomorphes de codimension un dont la classe canonique est triviale. Ann. Sci. Éc. Norm. Supér. (4) 41(4), 655–668 (2008)MathSciNetGoogle Scholar

Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Institut Camille JordanUniv Lyon, CNRS, Université Claude Bernard Lyon 1, UMR 5208VilleurbanneFrance

Personalised recommendations