Virtualconference
H Holomorphic Poisson structures - lecture 3
Auteurs : Pym, Brent (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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- POLISHCHUK, A. Algebraic geometry of Poisson brackets. Journal of Mathematical Sciences, 1997, vol. 84, no 5, p. 1413-1444. - https://doi.org/10.1007/BF02399197
- PYM, Brent. Constructions and classifications of projective Poisson varieties. Letters in mathematical physics, 2018, vol. 108, no 3, p. 573-632. - https://doi.org/10.1007/s11005-017-0984-5
- DUFOUR, Jean-Paul et ZUNG, Nguyen Tien. Poisson structures and their normal forms. Springer Science & Business Media, 2006. - https://doi.org/10.1007/b137493
- LAURENT-GENGOUX, Camille, PICHEREAU, Anne, et VANHAECKE, Pol. Poisson structures. Springer Science & Business Media, 2012. - https://doi.org/10.1007/978-3-642-31090-4
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Résumé :
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a particle is trapped.
I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.
I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.
Keywords : Poisson bracket; holomorphic foliation; algebraic variety
Codes MSC :
14J10
- Families, moduli, classification: algebraic theory
37F75
- Holomorphic foliations and vector fields
53D17
- Poisson manifolds; Poisson groupoids and algebroids
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-cirm_poisson_3.pdf
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-cirm_poisson_discussion.pdf
HOLOMORPHIC POISSON STRUCTURES - Pym, Brent
COMPLETE HOLOMORPHIC VECTOR FIELDS AND THEIR SINGULAR POINTS - Guillot, Adolfo
FANO FOLIATIONS - Druel, Stéphane; Aroujo, Carolina
CODIMENSION ONE FOLIATIONS WITH PSEUDO-EFFECTIVE CONORMAL BUNDLE - Touzet Frédéric
MINIMAL MODEL PROGRAM - Cascini, Paolo; Spicer, Calum
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 30/04/2020 Date de captation : 29/04/2020 Collection : Research School ; Algebraic and Complex Geometry Durée : 00:37:43 Domaine : Algebraic & Complex Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2020-04-28_Pym_Part3.mp4 
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Informations sur la Rencontre Virtuelle
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.cirm-math.com/virtual-event-2251.html;https://www.chairejeanmorlet.com/2020-1-...
Citation Data
DOI : 10.24350/CIRM.V.19630503Cite this video as: Pym, Brent (2020). Holomorphic Poisson structures - lecture 3.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19630503 URI : http://dx.doi.org/10.24350/CIRM.V.19630503 |
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