Birational unboundness of Q-Fano threefolds (following the work of Jiayuan Lin)

A class of varieties $B$ is birationally bounded if there exists a morphism $f: X \rightarrow S$ between two varieties such that every variety from $B$ is birational to one of the geometric fibres of $f$. We prove that the family of $\mathbb Q$-Fano threefolds with Picard number one is birationally unbounded.