English
Complete holomorphic vector fields and their singular points - lecture 1
Virtualconference
Auteurs : Guillot, Adolfo (Auteur de la Conférence)
CIRM (Editeur )
32C99 - None of the above but in this section
57S20 - Noncompact Lie groups of transformations
34M05 - Entire and meromorphic solutions (ODE)
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/flows_trans1.pdf
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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)
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/flows_trans1.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 15/05/2020 Date de captation : 14/05/2020 Sous collection : Research School arXiv category : Dynamical Systems ; Algebraic Geometry Domaine : Dynamical Systems & ODE ; Geometry Format : MP4 (.mp4) - HD Durée : 00:41:29 Audience : Researchers Download : https://videos.cirm-math.fr/2020-05-12_Guillot_Part1.mp4 
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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 feuilletagesOrganisateurs de la rencontre : Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan 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.19632403Citer cette vidéo: Guillot, Adolfo (2020). Complete holomorphic vector fields and their singular points - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19632403 URI : http://dx.doi.org/10.24350/CIRM.V.19632403 |
Voir aussi
- [Virtualconference] Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces / Auteur de la Conférence Mayrand, Maxence.
- [Virtualconference] MMP & foliations on 3-folds : applications / Auteur de la Conférence Svaldi, Roberto.
- [Virtualconference] Regular foliations on rationally connected manifolds / Auteur de la Conférence Figueredo, João Paulo.
- [Virtualconference] Boundedness of minimal partial du Val resolutions of canonical surface foliations / Auteur de la Conférence Chen, Yen-An.
- [Virtualconference] Topics on the Poisson varieties of dimension at least four / Auteur de la Conférence Okumura, Katsuhiko.
- [Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Auteur de la Conférence Jaoui, Rémi.
- [Virtualconference] On symmetries of transversely projective foliations / Auteur de la Conférence Lo Bianco, Federico.
- [Virtualconference] Higher Ramanujan foliations / Auteur de la Conférence Jardim Da Fonseca, Tiago.
- [Virtualconference] Dynamics of Jouanolou foliation / Auteur de la Conférence Deroin, Bertrand.
Bibliographie
- Richard S. Palais.; A global formulation of the Lie theory of transformation groups. Mem. Amer. Math. Soc. No., 22:iii+123, 1957. -
- Julio C. Rebelo. ; Singularités des flots holomorphes. Ann. Inst. Fourier (Grenoble), 46(2):411–428, 1996. - http://www.numdam.org/article/AIF_1996__46_2_411_0.pdf
- Adolfo Guillot. Vector fields, separatrices and Kato surfaces. Ann. Inst. Fourier (Grenoble), 64(3):1331–1361, 2014. - http://www.numdam.org/item/AIF_2014__64_3_1331_0/
- Adolfo Guillot and Julio Rebelo. Semicomplete meromorphic vector fields on complex surfaces. J. Reine Angew. Math., 667:27–65, 2012. - https://doi.org/10.1515/CRELLE.2011.127
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