ABCH's explicit Bridgeland–Mori wall correspondence conjecture for the Hilbert scheme

Let $I_Z$ be the ideal sheaf of a point $Z\in\mathbb{P}^{2[n]}$. A Bridgeland wall is a wall $W_x$ in the family of walls $W_{I_Z,(r',c',d')}$ along which some ideal sheaf $I_Z$ is destabilized. With $n$ fixed, such walls are parametrized by their centers $(x,0)$. A Mori wall is a ray

$$H+\frac{1}{2y}\Delta$$

in $\operatorname{Eff}(\mathbb{P}^{2[n]})$ where the stable base locus of a divisor changes; it is parametrized by $y<0$. ABCH's explicit wall correspondence conjecture. There is a one-to-one correspondence between Bridgeland walls $W_x$ and Mori walls $H+\frac{1}{2y}\Delta$ for $\mathbb{P}^{2[n]}$ given by

$$x=y-\frac{3}{2}.$$

This gives an explicit form of the conjectural correspondence between Bridgeland stability walls and Mori chamber walls, relating stability conditions to the birational geometry of the Hilbert scheme.