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arXiv · 2102.12641

A global Weinstein splitting theorem for holomorphic Poisson manifolds

Stéphane Druel·Jorge Vitório Pereira·Brent Pym·Frédéric Touzet
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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.

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Stéphane Druel, Jorge Vitório Pereira, Brent Pym, Frédéric Touzet. 2021-02-25. A global Weinstein splitting theorem for holomorphic Poisson manifolds. https://doi.org/10.2140/gt.2022.26.2831

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