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Audiovisual Mathematics Library

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Virtualconference

Authors : Mayrand, Maxence (Author of the conference)
CIRM (Publisher )

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Abstract : I will discuss the existence of hyperkähler structures on local symplectic groupoids integrating holomorphic Poisson manifolds, and show that they always exist when the base is a Poisson surface. The hyperkähler structure is obtained by constructing the twistor space by lifting specific deformations of the Poisson surface adapted from Hitchin's unobstructedness result. In the special case of the zero Poisson structure, we recover the Feix-Kaledin hyperkähler structure on the cotangent bundle of a Kähler manifold.

MSC Codes :
32G05 - Deformations of complex structures
53C26 - Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C28 - Twistor methods
53D17 - Poisson manifolds; Poisson groupoids and algebroids

Information on the Video

Film maker :

Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-05-28_Mayrand.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.19639503
Cite this video as: Mayrand, Maxence (2020). Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19639503
URI : http://dx.doi.org/10.24350/CIRM.V.19639503

See Also

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[Virtualconference] Topics on the Poisson varieties of dimension at least four / Author of the conference Okumura, Katsuhiko.
[Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Author of the conference Jaoui, Rémi.
[Virtualconference] On symmetries of transversely projective foliations / Author of the conference Lo Bianco, Federico.
[Virtualconference] Higher Ramanujan foliations / Author of the conference Jardim Da Fonseca, Tiago.
[Virtualconference] Dynamics of Jouanolou foliation / Author of the conference Deroin, Bertrand.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 4 / Author of the conference Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 3 / Author of the conference Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 1 / Author of the conference Guillot, Adolfo.
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[Virtualconference] Fano foliations 3 - Classification of Fano foliations of large index - lecture 4 / Author of the conference Araujo, Carolina.
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[Virtualconference] MMP for co-rank1 foliations - lecture 2 / Author of the conference Spicer, Calum.
[Virtualconference] MMP for co-rank1 foliations - lecture 1 / Author of the conference Spicer, Calum.
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[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 3 / Author of the conference Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 2 / Author of the conference Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 1 / Author of the conference Touzet, Frédéric.
[Virtualconference] Holomorphic Poisson structures - lecture 4 / Author of the conference Pym, Brent.
[Virtualconference] Fano foliations 2 - Adjunction formula and applications - lecture 3 / Author of the conference Druel, Stéphane.
[Virtualconference] Fano foliations 0 - Algebraicity of smooth formal schemes and applications to foliations - lecture 1 / Author of the conference Druel, Stéphane.
[Virtualconference] Holomorphic Poisson structures - lecture 3 / Author of the conference Pym, Brent.
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Bibliography

FEIX, B. Hyperkähler metrics on cotangent bundles. J. Reine Angew. Math. 532 (2001), 33–46. - https://doi.org/10.1515/crll.2001.017

GUALTIERI, M. Generalized Kähler metrics from Hamiltonian deformations. Geometry and physics. Vol. II, 551–579, Oxford Univ. Press, Oxford, 2018. -

HITCHIN, Nigel. Deformations of holomorphic Poisson manifolds. Moscow Mathematical Journal, 2012, vol. 12, no 3, p. 567-591. - https://doi.org/10.17323/1609-4514-2012-12-3-567-591

WEINSTEIN, Alan, et al. The local structure of Poisson manifolds. Journal of differential geometry, 1983, vol. 18, no 3, p. 523-557. - http://dx.doi.org/10.4310/jdg/1214437787

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