Collins–Jacob–Yau conjecture for the deformed Hermitian Yang–Mills equation

Let $X$ be a rational homogeneous variety of complex dimension $n$, let $[\psi]$ be a class with phase angle $\hat{\Theta}\in \big((n-2)\frac{\pi}{2},n\frac{\pi}{2}\big)$, and for an irreducible analytic subvariety $Y\varsubsetneq X$ let $Z_Y([\psi])$ denote its central charge. Collins–Jacob–Yau conjecture. There exists a solution to the deformed Hermitian Yang–Mills equation in the class $[\psi]$ with phase angle $\hat{\Theta}$ if and only if

$$\operatorname{Im}\left(\frac{Z_Y([\psi])}{Z_X([\psi])}\right)>0.$$

for every irreducible analytic subvariety $Y\varsubsetneq X_P$. In complex dimension two, the corresponding criterion is known for curves; the conjecture proposes its higher-dimensional analogue, while the general existence criterion remains open.