Campana’s rational-connectedness conjecture for klt Fano orbifolds
For every projective klt orbifold pair such that is ample, the orbifold is Campana rationally connected.
References
Primary source
Additional references
- Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds — arXiv — Saptarshi Dandapat
Progress summary
A September 2026 paper reports a proof for broad two-dimensional del Pezzo orbifold families; the general conjecture remains open.
Campana’s conjecture predicts rational connectedness for every klt Fano orbifold. The newly reported result concerns broad two-dimensional del Pezzo-orbifold families, not the full conjecture.
Known results
- Smooth projective toric varieties with their torus-invariant boundary satisfy the stronger property of strong Campana uniruledness, hence Campana rational connectedness; weak approximation also follows under suitable hypotheses (2024).
September 2026 del Pezzo-orbifold advance
Saptarshi Dandapat’s paper reports establishing the conjectural rational-connectedness statement for broad two-dimensional del Pezzo-orbifold families and deriving weak approximation for associated Campana fibrations. This is a claimed advance, not an independently verified solution of the general conjecture.
Current status (as of September 2026): the toric case is established, a broad two-dimensional del Pezzo-orbifold result is claimed but unverified, and the general klt Fano-orbifold conjecture remains open.
Solutions 0
No solutions have been posted yet.