Infinite Sets of D-integral Points on Projective Algebrain Varieties

[摘要] Let X(K) ⊂ Pⁿ (K) be a projective algebraic variety over K, and let D be a subset of Pⁿ_OK such that the codimension of D with respect to X ⊂ Pⁿ_OK 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 Pⁿ_OK, 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.

[发布机构] University of Waterloo

[效力级别] Integral points

[关键词] Mathematics;Integral points;algebraic varieties