Quasi-projectivity conjecture for singular Kähler–Ricci shrinkers

Let $(X,d_X)$ be the singular Kähler–Ricci shrinker arising as the metric soliton modeled on the $\mathbb{F}$-limit described in the paper, with regular part $(\mathcal{R}_X,g_X,\omega_X,J_X,f_X)$. Quasi-projectivity conjecture. $X$ admits a polarized Fano fibration structure and hence is a quasi-projective variety. This conjecture extends quasi-projectivity results for smooth Kähler–Ricci shrinkers to the singular setting and is motivated by boundedness results for Fano varieties; its resolution is not established in the supplied context.