Tohoku Mathematical Journal
2009
December
SECOND SERIES VOL. 61, NO. 4

Tohoku Math. J.
61 (2009), 589-601

Title INTEGRAL POINTS ON THREEFOLDS AND OTHER VARIETIES

Author Pietro Corvaja, Aaron Levin and Umberto Zannier

(Received October 28, 2008, revised July 3, 2009)
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.

2000 Mathematics Subject Classification. Primary 11G35; Secondary 14G25, 32H30, 11J97.
Key words and phrases. Integral points, holomorphic curves, Schmidt Subspace Theorem, Diophantine approximation.

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