Geodesic
A global Weinstein splitting theorem for holomorphic Poisson manifolds
Druel, Stéphane1 ; Pereira, Jorge Vitório2 ; Pym, Brent3 ; Touzet, Frédéric4
1 Institut Camille Jordan, CNRS, Université Claude Bernard Lyon 1, Villeurbanne, France
2 Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
3 Department of Mathematics and Statistics, McGill University, Montreal QC, Canada
4 Institut de recherche mathématique de Rennes, Université Rennes 1, Rennes, France
Geometry & topology, Tome 26 (2022) no. 6, pp. 2831-2853.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

Keywords: complex Poisson manifolds, complex foliations

Druel, Stéphane 1 ; Pereira, Jorge Vitório 2 ; Pym, Brent 3 ; Touzet, Frédéric 4

1 Institut Camille Jordan, CNRS, Université Claude Bernard Lyon 1, Villeurbanne, France
2 Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
3 Department of Mathematics and Statistics, McGill University, Montreal QC, Canada
4 Institut de recherche mathématique de Rennes, Université Rennes 1, Rennes, France 
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Druel, Stéphane; Pereira, Jorge Vitório; Pym, Brent; Touzet, Frédéric. A global Weinstein splitting theorem for holomorphic Poisson manifolds. Geometry & topology, Tome 26 (2022) no. 6, pp. 2831-2853. http://geodesic.mathdoc.fr/item/GT_2022_26_6_a8/

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