$S$-integral points of $\mathbb {P}^n-\{2n+1$ hyperplanes in general position over number fields and function fields}
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- by Julie T.-Y. Wang PDF
- Trans. Amer. Math. Soc. 348 (1996), 3379-3389 Request permission
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), 95β107). 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 βgenerators" of those $S$-integral points. The main tool here is the $S$-unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427β434).References
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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
- MR Author ID: 364623
- ORCID: 0000-0003-2133-1178
- Received by editor(s): November 7, 1994
- Received by editor(s) in revised form: July 10, 1995
- © Copyright 1996 American Mathematical Society
- 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