Abstract
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.
Citation
Stéphane Druel. Jorge Vitório Pereira. Brent Pym. Frédéric Touzet. "A global Weinstein splitting theorem for holomorphic Poisson manifolds." Geom. Topol. 26 (6) 2831 - 2853, 2022. https://doi.org/10.2140/gt.2022.26.2831
Information