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arXiv · 2308.11847

Approximating rational points on horospherical varieties

Sean Monahan·Matthew Satriano
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Abstract

Let $X$ be a smooth projective split horospherical variety over a number field $k$ and $x\in X(k)$. 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 $\mathbb{Q}$-factorial horospherical varieties with terminal singularities.

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Sean Monahan, Matthew Satriano. 2023-08-23. Approximating rational points on horospherical varieties. https://arxiv.org/abs/2308.11847

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