Absolute rigidity conjecture for divisorially canonical Fano varieties

Let $V$) be a divisorially canonical Fano variety, and let $X$ be a rationally connected variety with $\dim X=\dim V$. A rational dominant map is a rational map $X\dashrightarrow V$ whose image is dense. Absolute rigidity conjecture. Every such rational dominant map $X\dashrightarrow V$ is birational. This conjecture strengthens the paper's result for abelian rational Galois covers by predicting that all rational dominant maps of the same dimension are birational.