Characterization conjecture for weighted projective spaces as Fano orbifolds

Let $\mathcal{Y}$ be a Fano orbifold of dimension $n$. For $\ell eau0000\mathbb{Z}_{>0}$, let $g\bin a pi_0(I\mathcal{Y})$, and let $f$ be a twisted map in $\mathrm{Mor}_{(1,g)}(\mathbb{P}^1(1,\ell),\mathcal{Y})$. Define

$$d_{g^{-1}}(f)=-K_{\mathcal{Y}}\cdot f_*\mathbb{P}^1(1,\ell)+\operatorname{age}(g^{-1}).$$

Weighted-projective-space characterization conjecture. If, for every such $\ell$, $g$, and $f$,

$$d_{g^{-1}}(f)\ge n+1,$$

then $\mathcal{Y}$ is isomorphic to a finite quotient of a weighted projective space. The conjecture proposes a characterization of weighted projective spaces among Fano orbifolds; in the smooth case it is essentially the Mori–Mukai conjecture, proved by Cho, Miyaoka, and Shepherd-Barron. The general orbifold statement is therefore the unresolved extension proposed here.