4 problems

Wirsing's conjecture. For all transcendental $\xi$, the degree $\omega^*$ can be made arbitrarily close to $n+1$.

Modified Kodaira conjecture. There exists a bimeromorphic model

Bimeromorphic algebraic approximation conjecture. There exists a bimeromorphic map

Algebraic approximation conjecture. Every compact Kähler manifold is algebraically approximable.