论文标题
近似于感谢
Approximating rational points on toric varieties
论文作者
论文摘要
鉴于X（k）$中的数字字段$ k $上平滑的投射品种$ x $，第一作者猜想从精确的意义上说，任何近似$ p $的序列都必须在有理曲线上都足够好。我们证明了这种猜想，用于在Vojta的猜想上有条件的平滑分裂曲面表面。更笼统地，我们表明，如果$ x $是$ \ mathbb {q} $ - 段落终端折叠的图要折叠的多种尺寸，那么$ p $比任何zariski密度序列都比有理曲线上的点更好。
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.
