On closed 4-manifolds with b+2=1, Kodaira dimension zero, or negative curvature, holomorphically tamed symplectic forms with Kähler-type classes are Kähler, and Kähler-type forms in a fixed class are unique up to homologically trivial diffeomorphism.
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The spaces of K\"ahler and holomorphically tamed symplectic forms on closed 4-manifolds
On closed 4-manifolds with b+2=1, Kodaira dimension zero, or negative curvature, holomorphically tamed symplectic forms with Kähler-type classes are Kähler, and Kähler-type forms in a fixed class are unique up to homologically trivial diffeomorphism.