CIRM - Videos & books Library - Regular foliations on rationally connected manifolds

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Résumé : In this talk, we will consider the problem of classifying regular foliations on rationally connected manifolds over the complex numbers. Conjecturally, these foliations should have algebraic leaves. I will show this is true when the manifold has dimension three, and the foliation has codimension one and non pseudo-effective canonical bundle.

Keywords : foliations; MMP; 3-folds

Codes MSC :
14E30 - Minimal model program (Mori theory, extremal rays)
14J30 - 3-folds [See also 32Q25]
37F75 - Holomorphic foliations and vector fields

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https://videos.cirm-math.fr/2020-05-26_Figuerido.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages
Dates : 18/05/2020 - 22/05/2020
Année de la rencontre : 2020
URL Congrès : https://www.chairejeanmorlet.com/2251.html

Données de citation

DOI : 10.24350/CIRM.V.19639003
Citer cette vidéo: (2020). Regular foliations on rationally connected manifolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19639003
URI : http://dx.doi.org/10.24350/CIRM.V.19639003

Voir aussi

[Virtualconference] Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces / Auteur de la Conférence ....
[Virtualconference] MMP & foliations on 3-folds : applications / Auteur de la Conférence ....
[Virtualconference] Boundedness of minimal partial du Val resolutions of canonical surface foliations / Auteur de la Conférence ....
[Virtualconference] Topics on the Poisson varieties of dimension at least four / Auteur de la Conférence ....
[Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Auteur de la Conférence ....
[Virtualconference] On symmetries of transversely projective foliations / Auteur de la Conférence ....
[Virtualconference] Higher Ramanujan foliations / Auteur de la Conférence ....
[Virtualconference] Dynamics of Jouanolou foliation / Auteur de la Conférence ....
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 4 / Auteur de la Conférence ....
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 3 / Auteur de la Conférence ....
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 1 / Auteur de la Conférence ....
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 2 / Auteur de la Conférence ....
[Virtualconference] Fano foliations 3 - Classification of Fano foliations of large index - lecture 4 / Auteur de la Conférence ....
[Virtualconference] Fano foliations 1 - Definition, examples and first properties - lecture 2 / Auteur de la Conférence ....
[Virtualconference] MMP for co-rank1 foliations - lecture 2 / Auteur de la Conférence ....
[Virtualconference] MMP for co-rank1 foliations - lecture 1 / Auteur de la Conférence ....
[Virtualconference] MMP for foliations of rank one - lecture 2 / Auteur de la Conférence ....
[Virtualconference] An overview of the minimal model program - lecture 1 / Auteur de la Conférence ....
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 3 / Auteur de la Conférence ....
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 2 / Auteur de la Conférence ....
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 1 / Auteur de la Conférence ....
[Virtualconference] Holomorphic Poisson structures - lecture 4 / Auteur de la Conférence ....
[Virtualconference] Fano foliations 2 - Adjunction formula and applications - lecture 3 / Auteur de la Conférence ....
[Virtualconference] Fano foliations 0 - Algebraicity of smooth formal schemes and applications to foliations - lecture 1 / Auteur de la Conférence ....
[Virtualconference] Holomorphic Poisson structures - lecture 3 / Auteur de la Conférence ....
[Virtualconference] Holomorphic Poisson structures - lecture 2 / Auteur de la Conférence ....
[Virtualconference] Holomorphic Poisson structures - lecture 1 / Auteur de la Conférence ....

Bibliographie

BRUNELLA, Marco. Feuilletages holomorphes sur les surfaces complexes compactes. In : Annales Scientifiques de l'Ecole Normale Superieure. No longer published by Elsevier, 1997. p. 569-594. - https://doi.org/10.1016/S0012-9593(97)89932-6

CASCINI, Paolo et SPICER, Calum. MMP for co-rank one foliation on threefolds. arXiv preprint arXiv:1808.02711, 2018. - https://arxiv.org/abs/1808.02711

DRUEL, Stéphane. Regular foliations on weak Fano manifolds. In : Annales de la Faculté des sciences de Toulouse: Mathématiques. 2017. p. 207-217. - https://afst.centre-mersenne.org/article/AFST_2017_6_26_1_207_0.pdf

MORI, Shigefumi . (1982). Threefolds Whose Canonical Bundles Are Not Numerically Effective. Annals of Mathematics, 116(1), second series, 133-176. - http://dx.doi.org/10.2307/2007050

SPICER, Calum. Higher-dimensional foliated Mori theory. Compositio Mathematica, 2020, vol. 156, no 1, p. 1-38. - https://doi.org/10.1112/S0010437X19007681

SPICER, Calum et SVALDI, Roberto. Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds. arXiv preprint arXiv:1908.05037, 2019. - https://arxiv.org/abs/1908.05037

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