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Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces
(University of Waterloo, 2010-04-27)
We are interested in investigating the number of integral points on quadrics. First, we consider non-degenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with ...
Infinite Sets of D-integral Points on Projective Algebrain Varieties
(University of Waterloo, 2005)
Let X(K) ⊂ <strong>P</strong><sup>n</sup> (K) be a projective algebraic variety over K, and let D be a subset of <strong>P</strong><sup>n</sup><sub>OK</sub> such that the codimension of D with respect to X ⊂ <strong>P</strong><sup>n</sup><sub>OK</sub> 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 <strong>P</strong><sup>n</sup><sub>OK</sub>, 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....