Tohoku Mathematical Journal

Integral points on threefolds and other varieties

Pietro Corvaja, Aaron Levin, and Umberto Zannier

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Abstract

We prove sufficient conditions for the degeneracy of integral points on certain threefolds and other varieties of higher dimension. In particular, under a normal crossings assumption, we prove the degeneracy of integral points on an affine threefold with seven ample divisors at infinity. Analogous results are given for holomorphic curves. As in our previous works [2], [5], the main tool involved is Schmidt's Subspace Theorem, but here we introduce a technical novelty which leads to stronger results in dimension three or higher.

Article information

Source
Tohoku Math. J. (2) Volume 61, Number 4 (2009), 589-601.

Dates
First available in Project Euclid: 21 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1264084501

Digital Object Identifier
doi:10.2748/tmj/1264084501

Mathematical Reviews number (MathSciNet)
MR2598251

Zentralblatt MATH identifier
1250.11066

Subjects
Primary: 11G35: Varieties over global fields [See also 14G25]
Secondary: 14G25: Global ground fields 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22} 11J97: Analogues of methods in Nevanlinna theory (work of Vojta et al.)

Keywords
Integral points holomorphic curves Schmidt Subspace Theorem Diophantine approximation

Citation

Corvaja, Pietro; Levin, Aaron; Zannier, Umberto. Integral points on threefolds and other varieties. Tohoku Math. J. (2) 61 (2009), no. 4, 589--601. doi:10.2748/tmj/1264084501. https://projecteuclid.org/euclid.tmj/1264084501


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References

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