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Codimension one foliation with pseudo-effective conormal bundle - lecture 2
Virtualconference
Authors : Touzet, Frédéric (Author of the conference)
CIRM (Publisher )
37F75 - Holomorphic foliations and vector fields
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/touzetconormal2cirm.pdf
CIRM (Publisher )
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Abstract :
Let X be a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. Basic examples of such distributions are provided by the kernel of a holomorphic one form, necessarily closed when the ambient is projective. More generally, due to a theorem of Jean-Pierre Demailly, a distribution with conormal sheaf pseudoeffective is actually integrable and thus defines a codimension 1 holomorphic foliation F. In this series of lectures, we would aim at describing the structure of such a foliation, especially in the non abundant case, i.e when F cannot be defined by a holomorphic one form (even passing through a finite cover). It turns out that \F is the pull-back of one of the "canonical foliations" on a Hilbert modular variety. This result remains valid for "logarithmic foliated pairs''.
Keywords : holomorphic foliations; pseudo-effective line bundle; abundance
MSC Codes : Keywords : holomorphic foliations; pseudo-effective line bundle; abundance
37F75 - Holomorphic foliations and vector fields
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/touzetconormal2cirm.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/05/2020 Conference Date : 06/05/2020 Subseries : Research School arXiv category : Algebraic Geometry ; Dynamical Systems Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:40:29 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-05-06_Touzet_Part2.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletagesEvent Organizers : Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan Dates : 18/05/2020 - 22/05/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2251.html
Citation Data
DOI : 10.24350/CIRM.V.19631103Cite this video as: Touzet, Frédéric (2020). Codimension one foliation with pseudo-effective conormal bundle - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19631103 URI : http://dx.doi.org/10.24350/CIRM.V.19631103 |
See Also
- [Virtualconference] Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces / Author of the conference Mayrand, Maxence.
- [Virtualconference] MMP & foliations on 3-folds : applications / Author of the conference Svaldi, Roberto.
- [Virtualconference] Regular foliations on rationally connected manifolds / Author of the conference Figueredo, João Paulo.
- [Virtualconference] Boundedness of minimal partial du Val resolutions of canonical surface foliations / Author of the conference Chen, Yen-An.
- [Virtualconference] Topics on the Poisson varieties of dimension at least four / Author of the conference Okumura, Katsuhiko.
- [Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Author of the conference Jaoui, Rémi.
- [Virtualconference] On symmetries of transversely projective foliations / Author of the conference Lo Bianco, Federico.
- [Virtualconference] Higher Ramanujan foliations / Author of the conference Jardim Da Fonseca, Tiago.
- [Virtualconference] Dynamics of Jouanolou foliation / Author of the conference Deroin, Bertrand.
Bibliography
- Kevin Corlette, Carlos Simpson. On the classification of rank-two representations of quasiprojective fundamental groups. Compos. Math. 144 (2008), no. 5, 1271–1331 - https://doi.org/10.1112/S0010437X08003618
- Jean-Pierre Demailly. On the Frobenius integrability of certain holomorphic p-forms. Complex geometry (Göttingen, 2000), 93–98, Springer, Berlin, 2002. - http://dx.doi.org/10.1007/978-3-642-56202-0_6
- Frédéric Touzet. On the structure of codimension 1 foliations with pseudoeffective conormal bundle. Foliation theory in algebraic geometry, 157–216, Simons Symp., Springer, Cham, 2016. - http://dx.doi.org/10.1007/978-3-319-24460-0_7
- Frédéric Touzet. Uniformisation de l'espace des feuilles de certains feuilletages de codimension un. Bull. Braz. Math. Soc. (N.S.) 44 (2013), no. 3, 351–391. - https://doi.org/10.1007/s00574-013-0017-7
- Marco Brunella. Birational geometry of foliations. IMPA Monographs, 1. Springer, Cham, 2015. xiv+130 pp. - http://dx.doi.org/10.1007/978-3-319-14310-1
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