Campana rational connectedness and weak approximation

Qile Chen; Brian Lehmann; Sho Tanimoto

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arXiv · 2406.04991

Campana rational connectedness and weak approximation

Qile Chen·Brian Lehmann·Sho Tanimoto

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Abstract

Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation for Campana sections holds at places of good reduction when the general fiber satisfies a slightly stronger version of Campana rational connectedness. Campana also conjectured that any Fano orbifold is Campana rationally connected; we verify a stronger statement for toric Campana orbifolds. A key tool in our study is log geometry and moduli stacks of stable log maps.

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Qile Chen, Brian Lehmann, Sho Tanimoto. 2024-06-07. Campana rational connectedness and weak approximation. https://arxiv.org/abs/2406.04991

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