# Batyrev's theorem in non-algebraic case

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 $$n\geq 0$$?

• 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. – Jason Starr Dec 16 '18 at 14:52