Abstract:Let X be a smooth projective split horospherical variety over a number field k and x ∈ X(k). Contingent on Vojta's conjecture, we construct a curve C through x such that (in a precise sense) rational points on C approximate x better than any Zariski dense sequence of rational points. This proves a weakening of a conjecture of McKinnon in the horospherical case. Our results make use of the minimal model program and apply as well to Q-factorial horospherical varieties with terminal singularities.
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