For every Lagrangian fibration of a projective hyper-Kähler manifold, the perverse filtration equals the monodromy weight filtration of an associated type III degeneration.
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P=W for Lagrangian fibrations and degenerations of hyper-K\"ahler manifolds
For every Lagrangian fibration of a projective hyper-Kähler manifold, the perverse filtration equals the monodromy weight filtration of an associated type III degeneration.