PreprintarXiv licencearXiv
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.
Related
- Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds
- Smoothness criterion for Fano orbifolds and bases of Lagrangian fibrations
- Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$
- Analytic Construction of Rational Curves on Fano Manifolds
- Transverse rational curves and the homogeneity of contact Fano manifolds
BibTeX
@misc{lehmann2026fano,
title = {{Fano orbifolds admit free Campana curves}},
author = {Brian Lehmann and Sho Tanimoto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37513},
eprint = {2609.37513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37513},
}
RIS
TY - UNPB
TI - Fano orbifolds admit free Campana curves
AU - Brian Lehmann
AU - Sho Tanimoto
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.37513
UR - https://arxiv.org/abs/2609.37513
AB - 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.
ER -