2 problems

Popovici's conjecture. A limit of Kähler manifolds is of Fujiki class $\mathcal C$, that is, it is bimeromorphic to a Kähler manifold.

Let $X$ be a compact complex manifold of complex dimension $n$, and let $T$ be a closed positive $(1,1)$-current on $X$. Write $T_{ac}$ for its absolutely continuous part and…