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

Virtualconference

Authors : Okumura, Katsuhiko (Author of the conference)
CIRM (Publisher )

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Abstract : 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

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

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Hennenfent, Guillaume

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

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 feuilletages
Event 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.19638503
Cite this video as: 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

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Bibliography

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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