𝑆-integral points of ℙⁿ-{2𝕟+1 hyperplanes in general position over number fields and function fields}

Wang, Julie

doi:10.1090/S0002-9947-96-01568-1

$S$-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), 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).

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