On the density of rational and integral points on algebraic varieties

Journal article, 2007

Let X ⊂ ℙn be a projective geometrically integral variety over of dimension r and degree d ≧ 4. Suppose that there are only finitely many (r − 1)-planes over   on X. The main result of this paper is a proof of the fact that the number N(X;B) of rational points on Xwhich have height at most B satisfies   for any ɛ > 0. The implied constant depends at most on d, n and ɛ.