On the degree of integral points of a projective space minus a horizontal hypersurface

Let K be a number field of degree m with ring of integers R and absolute di scriminant d(K)? and (F) over bar = (F,p) a locally free R-module of rank s + 1, endowed with a Hermitian metric rho on F-C. Let deg((F) over bar) den ote the arithmetic degree of (F) over bar ([3], 2.1.3), and A ' (1)((F) ove r bar) the minimum of the supnorm associated to rho over all non-zero eleme nts of F. For a hypersurface Z(K) Of degree d in P(F-K), with Zariski closu re Z in P(F), we give an explicit function d(0) of m, d(K,) s, (deg) over c ap((F) over bar),d, and the projective height of Z as defined in [3], 4. 1, such that there exists an integral point of P(F)\Z of degree at most d(0).