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

Virtualconference

Authors : Figueredo, João Paulo (Author of the conference)
CIRM (Publisher )

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Abstract : 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

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

Information on the Video

Film maker :

Hennenfent, Guillaume

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

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 feuilletages
Event 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.19639003
Cite this video as: Figueredo, João Paulo (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

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Bibliography

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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