Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

Collection Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

Organizer(s) Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan

Date(s) 18/05/2020 - 22/05/2020

linked URL https://www.chairejeanmorlet.com/2251.html

00:00:00 / 00:00:00

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Complete holomorphic vector fields and their singular points - lecture 2

By Adolfo Guillot

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.

Information about the video

Date of recording 13/05/2020
Date of publication 15/05/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19632303
Cite this video Guillot, Adolfo (13/05/2020). Complete holomorphic vector fields and their singular points - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19632303
URL https://dx.doi.org/10.24350/CIRM.V.19632303

Domain(s)

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/

MSC codes

Document(s)

https://www.cirm-math.com/uploads/2/6/6/0/26605521/flows_trans2.pdf

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