The base projective-space conjecture for holomorphic Lagrangian fibrations

Let $X^{2n}$ be a hyperkähler manifold, and let $f:X\to B$ be a holomorphic Lagrangian fibration, where $B$ is its base. Base projective-space conjecture. If $X$ is a hyperkähler manifold and $f:X\to B$ is a holomorphic Lagrangian fibration, then

$$B\cong\mathbb{P}^n.$$

This conjecture concerns the structure of the base of a holomorphic Lagrangian fibration. The paper proves the assertion when the base is smooth, while the general case remains open.