2020/04/10 by McKinnon, David, Satriano, Matthew · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2004.05212
Given a smooth projective variety X over a number field k and P∈ 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 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.