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Infinite Sets of D-integral Points on Projective Algebrain Varieties

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vshelest2005.pdf (246.95 KB)

Date

2005

Authors

Shelestunova, Veronika

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University of Waterloo

Abstract

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

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Keywords

Mathematics, Integral points, algebraic varieties

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URI

http://hdl.handle.net/10012/1192

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Pure Mathematics