2 problems

Width-decreasing conjecture. Let $X$ be a CP-manifold which is not a product of positive-dimensional varieties. If $\tau(X)>0$, then there exists a surjective morphism $f:X'\to X$…

The LQEL classification conjecture. $X$ is obtained by taking linear sections and/or isomorphic projections of a rational homogeneous manifold in its natural minimal embedding.