Campana rational connectedness

The notion of Campana points were introduced by Campana and Abramovich, which interpolate between rational points and integral points. In this talk, we will focus on the geometric side and introduce Campana rational connectedness — a version of rational connectedness for varieties with simple normal crossings boundaries. We further prove that over function fields, weak approximations by Campana points at good places hold assuming Campana rational connectedness of fibers, generalizing a theorem of Hassett and Tschinkel. We further verify Campana rational connectedness for many basic examples. Our approach relies on the theory of stable log maps and their moduli. This is a joint work in progress with Brian Lehmann and Sho Tanimoto.

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