2 problems

Let $X$ be a compact complex manifold of dimension $n$, and let $H^{1,1}_{BC}(X,\mathbb C)$ denote its complex Bott–Chern $(1,1)$-cohomology. A class is nef if it lies in the nef c…

The Hodge conjecture in Bott-Chern cohomology. Every element of $H^{p,p}_{BC}(Y;\Q)$ is representable by holomorphic $p$-chains with $\Q$-coefficients.