Source: Tohoku Math. J. (2) Volume 61, Number 4
(2009), 589-601.
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.
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References
P. Autissier, Géométrie, points entiers et courbes entières, Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), 221--239.
P. Corvaja and U. Zannier, On the number of integral points on algebraic curves, J. Reine Angew. Math. 565 (2003), 27--42.
P. Corvaja and U. Zannier, On integral points on surfaces, Ann. of Math. (2) 160 (2004), 705--726.
O. Debarre, Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, New York, 2001.
A. Levin, Generalizations of Siegel's and Picard's theorem, Ann. of Math. (2) 170 (2009), 609--655.
P. Vojta, A refinement of Schmidt's subspace theorem, Amer. J. Math. 111 (1989), 489--518.
P. Vojta, Integral points on subvarieties of semiabelian varieties. I, Invent. Math. 126 (1996), 133--181.
P. Vojta, On Cartan's theorem and Cartan's conjecture, Amer. J. Math. 119 (1997), 1--17.
