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Greatest common
divisors of integral points of numerically equivalent
divisors
Julie Tzu-Yueh Wang and Yu Yasufuku |
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Vol. 15 (2021), No. 1, 287–305
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Abstract |
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We generalize the gcd results of Corvaja and Zannier and of Levin on to more general settings. More specifically, we analyze the height of a closed subscheme of codimension at least inside an -dimensional Cohen–Macaulay projective variety, and show that this height is small when evaluated at integral points with respect to a divisor when is a sum of effective divisors which are all numerically equivalent to some multiples of a fixed ample divisor. Our method is inspired by Silverman’s gcd estimate, but instead of his usage of Vojta’s conjecture, we use the recent result of Ru and Vojta. |
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Keywords
height inequality, integral points, greatest common
divisors, blowups, Schmidt subspace theorem, Vojta's
conjecture, entire curves
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Mathematical Subject Classification 2010
Primary: 11J97
Secondary: 11J87, 14G05, 32A22
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Milestones
Received: 25 February 2020
Revised: 2 May 2020
Accepted: 2 July 2020
Published: 1 March 2021
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Authors |
| Julie Tzu-Yueh Wang | |
| Institute of Mathematics Academia Sinica Taipei Taiwan |
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| Yu Yasufuku | |
| Department of Mathematics, College
of Science and Technology Nihon University Chiyoda-ku, Tokyo Japan |
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