Miranda's conjecture on Chow stability of rational Weierstrass fibrations

Let $W$ be a rational Weierstrass fibration, let $X$ be its minimal resolution, and let $H$ be an arbitrary ample line bundle. Miranda's conjecture. The pair $(W,H)$ is asymptotically Chow-stable if $X$ has only reduced fibers, asymptotically Chow-semistable if $X$ has only reduced and $I_N^*$-type fibers for $N\ge0$, and asymptotically Chow-unstable if $X$ has at least one $II^*$-, $III^*$- or $IV^*$-type fiber. This conjecture predicts that asymptotic Chow stability is determined by the fiber types of the associated rational elliptic surface; the paper applies its results to this conjecture.