Diophantine Approximation Constants for Varieties over Function Fields

Abstract

By analogy with the program of McKinnon and Roth [10], we define and study approximation constants for points of a projective variety $X$ defined over $\mathbf{K}$, the function field of an irreducible and nonsingular in codimension $1$ projective variety defined over an algebraically closed field of characteristic zero. In this setting, we use Wang’s theorem, which is an effective version of Schmidt’s subspace theorem, to give a sufficient condition for such approximation constants to be computed on a proper $\mathbf{K}$-subvariety of $X$. We also indicate how our approximation constants are related to volume functions and Seshadri constants.