Tohoku Mathematical Journal

Integral points on threefolds and other varieties

Pietro Corvaja, Aaron Levin, and Umberto Zannier

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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

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

First available in Project Euclid: 21 January 2010

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Zentralblatt MATH identifier

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.)

Integral points holomorphic curves Schmidt Subspace Theorem Diophantine approximation


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.

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