Certain degeneration limits of Calabi-Yau and hyperkähler manifolds with bounded periods remain Kähler, giving new proofs and complete solutions to the Soldatenkov-Verbitsky and Perego conjectures.
Todorov, Applications of the K¨ ahler-Einstein-Calabi-Yau metric to moduli of K3 surfaces, Invent
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Degenerations and Stability of K\"ahler Structures on Calabi--Yau Manifolds
Certain degeneration limits of Calabi-Yau and hyperkähler manifolds with bounded periods remain Kähler, giving new proofs and complete solutions to the Soldatenkov-Verbitsky and Perego conjectures.