A global Weinstein splitting theorem for holomorphic Poisson manifolds
Algebraic Geometry
2022-12-21 v1 Differential Geometry
Symplectic Geometry
Abstract
We prove that if a compact K\"ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite \'etale 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 K\"ahler manifolds with split tangent bundle.
Cite
@article{arxiv.2102.12641,
title = {A global Weinstein splitting theorem for holomorphic Poisson manifolds},
author = {Stéphane Druel and Jorge Vitório Pereira and Brent Pym and Frédéric Touzet},
journal= {arXiv preprint arXiv:2102.12641},
year = {2022}
}
Comments
19 pages, comments welcome