A conjecture on rational approximations to rational points
David McKinnon · Journal of Algebraic Geometry · 2006
In this paper, we examine how well a rational point P P on an algebraic variety X X can be approximated by other rational points. We conjecture that if P P lies on a rational curve, then the best approximations to P P on X X can be chosen to lie along a rational curve. We prove this conjecture for a wide range of examples, and for a great many more examples we deduce our conjecture from Vojta’s Main Conjecture.