Bogomolov-Guan manifolds have unobstructed holomorphically symplectic deformations and admit a Beauville-Bogomolov-Fujiki form satisfying the Fujiki formula.
Angella, Cohomological Aspects in Complex Non-K\"ahler Geometry , Lecture Notes in Mathematics 2095, Springer, 2014
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Deformations and BBF form on non-Kahler holomorphically symplectic manifolds
Bogomolov-Guan manifolds have unobstructed holomorphically symplectic deformations and admit a Beauville-Bogomolov-Fujiki form satisfying the Fujiki formula.