CIRM - Videos & books Library - Topics on the Poisson varieties of dimension at least four

Virtualconference

Auteurs : Okumura, Katsuhiko (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : It is thought that the classifications and constructions of holomorphic Poisson structures are worth studying. The classification when the Picard rank is 2 or higher is unknown. In this talk, we will introduce the classification of holomorphic Poisson structures with the reduced degeneracy divisor that have only simple normal crossing singularities, on the product of Fano variety of Picard rank 1. This claims that such a Poisson manifold must be a diagonal Poisson structure on the product of projective spaces, so this is a generalization of Lima and Pereira's study. The talk will also include various examples, classifications, and problems of high-dimensional holomorphic Poisson structures.

Keywords : Poisson structure; log symplectic; characterization of projective space

Codes MSC :
14C17 - Intersection theory
14J45 - Fano varieties
53D17 - Poisson manifolds; Poisson groupoids and algebroids

Informations sur la Vidéo

Réalisateur :

Hennenfent, Guillaume

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

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 feuilletages
Organisateurs 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.19638503
Citer cette vidéo: Okumura, Katsuhiko (2020). Topics on the Poisson varieties of dimension at least four. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19638503
URI : http://dx.doi.org/10.24350/CIRM.V.19638503

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] 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.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 4 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 3 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 1 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 2 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Fano foliations 3 - Classification of Fano foliations of large index - lecture 4 / Auteur de la Conférence Araujo, Carolina.
[Virtualconference] Fano foliations 1 - Definition, examples and first properties - lecture 2 / Auteur de la Conférence Araujo, Carolina.
[Virtualconference] MMP for co-rank1 foliations - lecture 2 / Auteur de la Conférence Spicer, Calum.
[Virtualconference] MMP for co-rank1 foliations - lecture 1 / Auteur de la Conférence Spicer, Calum.
[Virtualconference] MMP for foliations of rank one - lecture 2 / Auteur de la Conférence Cascini, Paolo.
[Virtualconference] An overview of the minimal model program - lecture 1 / Auteur de la Conférence Cascini, Paolo.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 3 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 2 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 1 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Holomorphic Poisson structures - lecture 4 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Fano foliations 2 - Adjunction formula and applications - lecture 3 / Auteur de la Conférence Druel, Stéphane.
[Virtualconference] Fano foliations 0 - Algebraicity of smooth formal schemes and applications to foliations - lecture 1 / Auteur de la Conférence Druel, Stéphane.
[Virtualconference] Holomorphic Poisson structures - lecture 3 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Holomorphic Poisson structures - lecture 2 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Holomorphic Poisson structures - lecture 1 / Auteur de la Conférence Pym, Brent.

Bibliographie

LIMA, Renan et PEREIRA, Jorge Vitório. A characterization of diagonal Poisson structures. Bulletin of the London Mathematical Society, 2014, vol. 46, no 6, p. 1203-1217. - https://doi.org/10.1112/blms/bdu074

LORAY, Frank, PEREIRA, Jorge Vitório, et TOUZET, Frédéric. Foliations with trivial canonical bundle on Fano 3‐folds. Mathematische Nachrichten, 2013, vol. 286, no 8‐9, p. 921-940. - https://doi.org/10.1002/mana.201100354

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

PYM, Brent. Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets. Compositio Mathematica, 2017, vol. 153, no 4, p. 717-744. - https://doi.org/10.1112/S0010437X16008174

OKUMURA, Katsuhiko. SNC log symplectic structures on Fano products. Canadian Mathematical Bulletin, 2018, p. 1-10. - https://doi.org/10.4153/S0008439520000120

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