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arXiv · 1601.03825

Vojta's Conjecture on Multiple Blowups of $\mathbb{P}^2$ and the $abc$ conjecture

Yu Yasufuku
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Abstract

We show that Vojta's conjecture for some rational surfaces is related to the $abc$ conjecture. More specifically, we prove that Vojta's conjecture on these surfaces implies a special case of the $abc$ conjecture, while the $abc$ conjecture implies Vojta's conjecture on these surfaces. Moreover, for similar but different rational surfaces, we prove Vojta's conjecture unconditionally. To prove these results, we use some (possibly new) properties of Farey sequences.

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BibTeXRIS

Yu Yasufuku. 2016-01-15. Vojta's Conjecture on Multiple Blowups of $\mathbb{P}^2$ and the $abc$ conjecture. https://arxiv.org/abs/1601.03825

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