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A
global Weinstein splitting theorem for holomorphic Poisson
manifolds
Stéphane Druel, Jorge Vitório Pereira, Brent Pym and Frédéric Touzet |
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Geometry & Topology 26 (2022) 2831–2853
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DOI: 10.2140/gt.2022.26.2831
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Abstract |
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We prove that if a compact Kähler Poisson manifold has a compact symplectic leaf with finite fundamental group, then, after passing to a finite étale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson manifold. As a step in the proof, we establish a special case of Beauville’s conjecture on the structure of compact Kähler manifolds with split tangent bundle. |
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Keywords
complex Poisson manifolds, complex foliations
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Mathematical Subject Classification
Primary: 53D17
Secondary: 32J27, 37F75
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References |
Publication
Received: 12 March 2021
Revised: 5 July 2021
Accepted: 5 August 2021
Published: 13 December 2022
Proposed: Leonid Polterovich
Seconded: Richard P Thomas, Paul Seidel
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Authors |
| Stéphane Druel | |
| Institut Camille Jordan CNRS Université Claude Bernard Lyon 1 Villeurbanne France |
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| Jorge Vitório Pereira | |
| Instituto de Matemática Pura e
Aplicada Rio de Janeiro Brazil |
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| Brent Pym | |
| Department of Mathematics and
Statistics McGill University Montreal QC Canada |
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| Frédéric Touzet | |
| Institut de recherche mathématique
de Rennes Université Rennes 1 Rennes France |
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