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Complete holomorphic vector fields and their singular points - lecture 2
Virtualconference
Authors : Guillot, Adolfo (Author of the conference)
CIRM (Publisher )
32C99 - None of the above but in this section
57S20 - Noncompact Lie groups of transformations
34M05 - Entire and meromorphic solutions (ODE)
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/flows_trans2.pdf
CIRM (Publisher )
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Abstract :
On a complex manifold, complex flows induce complete holomorphic vector fields. However, only very seldomly a vector field integrates into a flow. In general, it is difficult to say whether a holomorphic vector field on a non-compact manifold is complete or not (vector fields on compact manifolds are always complete). Some twenty-five years ago, Rebelo realized an exploited the fact that there are local (and not just global!) obstructions for a vector field to be complete. This opened the door for a local study of complete holomorphic vector fields on complex manifolds. In this series of talks we will explore some of these results.
What I will talk about is for the greater part contained or summarized in the articles in the bibliography. Their introductions might be useful as a first reading on the subject.
Keywords : holomorphic vector field; completeness
MSC Codes : What I will talk about is for the greater part contained or summarized in the articles in the bibliography. Their introductions might be useful as a first reading on the subject.
Keywords : holomorphic vector field; completeness
32C99 - None of the above but in this section
57S20 - Noncompact Lie groups of transformations
34M05 - Entire and meromorphic solutions (ODE)
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/flows_trans2.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/05/2020 Conference Date : 13/05/2020 Subseries : Research School arXiv category : Dynamical Systems ; Algebraic Geometry Mathematical Area(s) : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:44:08 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-05-12_Guillot_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.19632303Cite this video as: Guillot, Adolfo (2020). Complete holomorphic vector fields and their singular points - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19632303 URI : http://dx.doi.org/10.24350/CIRM.V.19632303 |
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
- Ghys, Étienne; Rebelo, Julio C. Singularités des flots holomorphes. II. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1117-1174 - http://dx.doi.org/10.5802/aif.1594
- Rebelo, Julio C. Réalisation de germes de feuilletages holomorphes par des champs semi-complets en dimension 2. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 9 (2000) no. 4, pp. 735-763 - http://www.numdam.org/item/AFST_2000_6_9_4_735_0/
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