Abstract
In this note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.
Similar content being viewed by others
References
Araujo, C., Druel, S.: On fano foliations. Adv. Math. 238, 70–118 (2013)
Araujo, C., Druel, S.: On codimension 1 del Pezzo foliations on varieties with mild singularities. Math. Ann. 360(3–4), 769–798 (2014)
Campana, F., Păun, M.: Foliations with positive slopes and birational stability of orbifold cotangent bundles, preprint. arXiv:1508:0245v4 (2015)
Demailly, J.-P., Peternell, T., Schneider, M.: Pseudo-effective line bundles on compact Kähler manifolds. Internat. J. Math. 12(6), 689–741 (2001)
Druel, S.: Regular foliations on weak fano manifold, Ann. Fac. Sci. Toulouse Math. (6) 26(1), 207–217 (2017a)
Druel, S.: On foliations with nef anti-canonical bundle. Trans. A. Math. Soc. 369(11), 7765–7787 (2017b)
Druel, S.: Some remarks on regular foliations with numerically trivial canonical class, EPIGA 1 (2017c)
Druel, S.: Codimension one foliations with numerically trivial canonical class on singular spaces, preprint arXiv:1809.06905 (2018)
Druel, S.: A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Invent. Math. 211(1), 245–296 (2018)
Graber, T., Harris, J., Starr, J.: Families of rationally connected varieties. J. Am. Math. Soc. 16(1), 57–67 (2003). (electronic)
Loray, F., Pereira, J.V., Touzet, F.: Singular foliations with trivial canonical class. Invent. Math. 213(3), 1327–1380 (2018)
Pereira, J.V., Touzet, F.: Foliations with vanishing Chern classes. Bull. Braz. Math. Soc. (N.S.) 44(4), 731–754 (2013)
Touzet, F.: Feuilletages holomorphes de codimension un dont la classe canonique est triviale. Ann. Sci. Éc. Norm. Supér. (4) 41(4), 655–668 (2008)
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Druel, S. On Foliations with Semi-positive Anti-canonical Bundle. Bull Braz Math Soc, New Series 50, 315–321 (2019). https://doi.org/10.1007/s00574-018-00128-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00574-018-00128-7