Fano orbifolds admit free Campana curves

Abstract

We prove that any Fano orbifold admits a free Campana curve in the sense of Campana. Moreover, assuming that any klt log Fano pair admits a very free rational curve in its smooth locus, we prove that any Fano orbifold is Campana rationally connected. As an application, we prove the finiteness of the orbifold fundamental groups for Fano orbifolds.

arXiv commentWe added more references to similar constructions to Theorem 1.4 and expanded AI disclosure, 13 pages