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Let $X$ and $Y$ be two bimeromorphic closed Kaehler manifolds with trivial real $c_1$. Is it true that $b_n(X)=b_n(Y)$ for $n\geq 0$?

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    $\begingroup$ Welcome, new contributor. One of my colleagues points out that for hyperKaehler manifolds, this result is true regardless of algebraicity, since then the manifolds are even deformation equivalent. $\endgroup$ Dec 16, 2018 at 14:52

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