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.
Publié le : 2009-05-15
Classification:
Integral points,
holomorphic curves,
Schmidt Subspace Theorem,
Diophantine approximation,
11G35,
14G25,
32H30,
11J97
@article{1264084501,
author = {Corvaja, Pietro and Levin, Aaron and Zannier, Umberto},
title = {Integral points on threefolds and other varieties},
journal = {Tohoku Math. J. (2)},
volume = {61},
number = {1},
year = {2009},
pages = { 589-601},
language = {en},
url = {http://dml.mathdoc.fr/item/1264084501}
}
Corvaja, Pietro; Levin, Aaron; Zannier, Umberto. Integral points on threefolds and other varieties. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp. 589-601. http://gdmltest.u-ga.fr/item/1264084501/