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$S$-integral points of $\mathbb {P}^n-\{ 2n+1\text { hyperplanes in general position}\}$
over number fields and function fields


Author: Julie T.-Y. Wang
Journal: Trans. Amer. Math. Soc. 348 (1996), 3379-3389
MSC (1991): Primary 14G05; Secondary 11R58
DOI: https://doi.org/10.1090/S0002-9947-96-01568-1
MathSciNet review: 1340189
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Abstract | References | Similar Articles | Additional Information

Abstract: For the number field case we will give an upper bound on the number of the $S$-integral points in $\mathbb {P}^n(K)-\{ 2n+1\text { hyperplanes in general}$
$\text {position}\}$. The main tool here is the explicit upper bound of the number of solutions of $S$-unit equations (Invent. Math. 102 (1990), 95--107). For the function field case we will give a bound on the height of the $S$-integral points in $\mathbb {P}^n(K)-\{ 2n+1\text { hyperplanes in general position}\}$. We will also give a bound for the number of ``generators" of those $S$-integral points. The main tool here is the $S$-unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427--434).


References [Enhancements On Off] (What's this?)

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Additional Information

Julie T.-Y. Wang
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

DOI: https://doi.org/10.1090/S0002-9947-96-01568-1
Keywords: $S$-integral points of $\mathbb{P}^n(K)-\{ 2n+1\text{ hyperplanes in general position}\}$
Received by editor(s): November 7, 1994
Received by editor(s) in revised form: July 10, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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