Let <em>X</em>(<em>K</em>) ⊂ <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> ⊂ <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>.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/1192 |
| Date | January 2005 |
| Creators | Shelestunova, Veronika |
| Publisher | University of Waterloo |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | Dutch |
| Type | Thesis or Dissertation |
| Format | application/pdf, 252872 bytes, application/pdf |
| Rights | Copyright: 2005, Shelestunova, Veronika . All rights reserved. |
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