研究情報

Campana and Abramovich introduced the notion of Campana points which interpolate between rational points and integral points. Recently there are extensive activities on arithmetic geometry of Campana points and many conjectures have been proposed. In this talk we discuss Campana curves/sections in the geometric setting. Campana introduced the notion of Campana rationally connectedness and conjectured that any klt Fano orbifold is Campana rationally connected.. We prove that weak approximation at good places holds in the setting of Campana sections for any Campana rationally connected fibration. This is a generalization of theorems by Graber-Harris-Starr and Hassett-Tschinkel. A Key tool to this theorem is log geometry and the notion of moduli stack of stable log maps. Finally we verify Campana's conjecture for certain classes of orbifolds. This is work in progress which is joint with Qile Chen and Brian Lehmann.