PreprintCC BY-NC-ND 4.0arXiv
Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds
Abstract
We prove that a del Pezzo orbifold of degree less than 7, and del Pezzo orbifolds of higher degree with irreducible boundary are strongly Campana uniruled, and deduce that it is Campana rationally connected. This provides important non-toric examples in dimension two of a conjecture by Campana, in the form required by the weak approximation theorem, and yields weak approximation for Campana sections of Campana fibrations at all places whose general fibre is such an orbifold. In three appendices we classify the del Pezzo orbifolds of degree 6, 7 and 8 with irreducible boundary.
Related
BibTeX
@misc{dandapat2026campana,
title = {{Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds}},
author = {Saptarshi Dandapat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11533},
eprint = {2609.11533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11533},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds
AU - Saptarshi Dandapat
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11533
UR - https://arxiv.org/abs/2609.11533
AB - We prove that a del Pezzo orbifold of degree less than 7, and del Pezzo orbifolds of higher degree with irreducible boundary are strongly Campana uniruled, and deduce that it is Campana rationally connected. This provides important non-toric examples in dimension two of a conjecture by Campana, in the form required by the weak approximation theorem, and yields weak approximation for Campana sections of Campana fibrations at all places whose general fibre is such an orbifold. In three appendices we classify the del Pezzo orbifolds of degree 6, 7 and 8 with irreducible boundary.
ER -