Infinite Sets of D-integral Points on Projective Algebrain Varieties

by Shelestunova, Veronika

Let X(K) ⊂ Pn (K) be a projective algebraic variety over K, and let D be a subset of PnOK such that the codimension of D with respect to X ⊂ PnOK is two. We are interested in points P on X(K) with the property that the intersection of the closure of P and D is empty in PnOK, we call such points D-integral points on X(K). First we prove that certain algebraic varieties have infinitely many D-integral points. Then we find an explicit description of the complete set of all D-integral points in projective n-space over Q for several types of D.