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.
Bogomolov, On Guan’s examples of simply connected non-K¨ ahler compact complex manifolds, Amer
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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.