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\(P = W\) for Lagrangian fibrations and degenerations of hyper-Kähler manifolds. (English) Zbl 1467.14101

Summary: We identify the perverse filtration of a Lagrangian fibration with the monodromy weight filtration of a maximally unipotent degeneration of compact hyper-Kähler manifolds.

MSC:

14J42 Holomorphic symplectic varieties, hyper-Kähler varieties
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D06 Fibrations, degenerations in algebraic geometry
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