Existence of covering families of orbifold rational curves

Establish the existence of covering families of Campana rational curves for general klt Campana orbifolds with ample log anticanonical divisor.

Background

The paper explains that strong Campana uniruledness and the construction of free Campana curves are central to proving Campana rational connectedness. Although several special cases are known, the general existence of dominating families of Campana rational curves remains unresolved.

This is presented as a broader unresolved issue underlying approaches to Campana's rational connectedness conjecture, beyond the specific low-degree del Pezzo orbifolds classified in the paper.

References

In general, even the existence of covering families of orbifold rational curves is unknown, which led Campana to introduce a slope-theoretic substitute for rational connectedness of orbifolds.

— Classification of low degree del Pezzo orbifolds II  (2610.06357 - Dandapat, 5 Oct 2026) in Section 1, subsection “Campana's rational connectedness conjecture”