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.
Verbitsky, Mapping class group and a global Torelli theorem for hyperk¨ ahler manifolds: an erratum,Duke Math
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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.