Every locally free Poisson module on a klt Poisson projective variety is rationally Morita equivalent to a flat partial sheaf, a meromorphic flat connection, a co-Higgs sheaf, or a special meromorphic co-Higgs sheaf.
Beauville, Holomorphic symplectic geometry: a problem list
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Rational Morita equivalence for holomorphic Poisson modules
Every locally free Poisson module on a klt Poisson projective variety is rationally Morita equivalent to a flat partial sheaf, a meromorphic flat connection, a co-Higgs sheaf, or a special meromorphic co-Higgs sheaf.