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arXiv · 2004.05212

Approximating rational points on toric varieties

David McKinnon·Matthew Satriano
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Abstract

Given a smooth projective variety $X$ over a number field $k$ and $P\in X(k)$, the first author conjectured that in a precise sense, any sequence that approximates $P$ sufficiently well must lie on a rational curve. We prove this conjecture for smooth split toric surfaces conditional on Vojta's conjecture. More generally, we show that if $X$ is a $\mathbb{Q}$-factorial terminal split toric variety of arbitrary dimension, then $P$ is better approximated by points on a rational curve than by any Zariski dense sequence.

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David McKinnon, Matthew Satriano. 2020-04-10. Approximating rational points on toric varieties. https://arxiv.org/abs/2004.05212

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