Abstract
Let Κ be a field and H be a set of hyperplanes in P n (Κ). When Κ is a function field, we show that the following are equivalent, (a) H is nondegenerate over Κ. (b) The height of the (S, H)-integral points of P n (Κ) - H is bounded. (c) P n Κ - H is an abc variety. When Κ is a number field and H is nondegenerate over Κ, we establish an explicit bound on the number of (S, H)-integral points of P n (Κ) - H. Finally, we discuss the geometric properties of holomorphic maps into P n (ℂ) omitting a set of hyperplanes with moving targets.