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
21 28

Topics on the Poisson varieties of dimension at least four

By Katsuhiko Okumura

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19638503
  • Cite this video Okumura, Katsuhiko (26/05/2020). Topics on the Poisson varieties of dimension at least four. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19638503
  • URL https://dx.doi.org/10.24350/CIRM.V.19638503

Domain(s)

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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