Diophantine approximation constants for varieties over function fields

By analogy with the program of McKinnon-Roth, we define and study approximation constants for points of a projective variety X defined over K the function field of an irreducible and non-singular in codimension 1 projective variety defined over an algebraically closed field of characteristic zero. In this setting, we use an effective version of Schmidt's subspace theorem, due to J.T.-Y. Wang, to give a sufficient condition for such approximation constants to be computed on a proper K-subvariety of X. We also indicate how our approximation constants are related to volume functions and Seshadri constants.