Strong Campana uniruledness conjecture for Fano orbifolds

Let (X,Δϵ)(X,\Delta_\epsilon) be a klt Campana orbifold over a field of characteristic 00. It is strongly Campana uniruled when there exists a free Campana curve f:CXf:C\to X such that the class f[C]f_*[C] lies in the interior of the nef cone Nef1(X)\operatorname{Nef}_1(X) of curves. Strong Campana uniruledness conjecture. Every klt Fano orbifold (X,Δϵ)(X,\Delta_\epsilon) is strongly Campana uniruled. This stronger conjecture is introduced for the paper's applications; the supplied text gives no resolution, so its general status remains open.

Sources & referencesView supporting material

Primary source

Qile Chen, Brian Lehmann and Sho Tanimoto, “Campana rational connectedness and weak approximation”, arXiv:2406.04991 (2025).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.