Orbifold Green–Griffiths–Lang conjecture

Let $\mathcal{X}$ be an orbifold, and let $\mathcal{Z}\subset\mathcal{X}$ be a sub-orbifold. A holomorphic map $f:{\mathbb C}\to\mathcal{X}$ is an orbifold entire curve.

Orbifold Green–Griffiths–Lang conjecture. If $\mathcal{X}$ is of general type, then there exists a proper sub-orbifold $\mathcal{Z}\subset\mathcal{X}$ containing the image of every holomorphic map $f:{\mathbb C}\to\mathcal{X}$.

This generalizes the Green–Griffiths–Lang conjecture from varieties to orbifolds. The paper presents it as a proposed generalization, and its general status is open.