The Dimensions of Integral Points and Holomorphic Curves on the Complements of Hyperplanes

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dc.creatorLevin, Aaron
dc.date2006-01-27
dc.date.accessioned2026-07-07T06:59:25Z
dc.date.available2026-07-07T06:59:25Z
dc.descriptionIn this article we completely determine the possible dimensions of integral points and holomorphic curves on the complement of a union of hyperplanes in projective space. Our main theorems generalize a result of Evertse and Gyory, who determined when all sets of integral points (over all number fields) on the complement of a union of hyperplanes are finite, and a result of Ru, who determined when all holomorphic maps to the complement of a union of hyperplanes are constant. The main tools used are the S-unit lemma and its analytic analogue, Borel's lemma.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0601691
dc.identifierhttp://arxiv.org/abs/math/0601691
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107738
dc.subjectNumber Theory
dc.subjectComplex Variables
dc.subject11D57; 11D72; 32H30
dc.titleThe Dimensions of Integral Points and Holomorphic Curves on the Complements of Hyperplanes
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