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arXiv · 1609.05091

Bounding heights uniformly in families of hyperbolic varieties

Kenneth Ascher·Ariyan Javanpeykar
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Abstract

We show that, assuming Vojta's height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded "uniformly" in families. This generalizes a result of Su-Ion Ih for curves of genus at least two to higher-dimensional varieties. As an application, we show that, assuming Vojta's height conjecture, the height of a rational point on a curve of general type is uniformly bounded. Finally, we prove a similar result for smooth hyperbolic surfaces with $c_1^2 > c_2$.

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Kenneth Ascher, Ariyan Javanpeykar. 2016-09-16. Bounding heights uniformly in families of hyperbolic varieties. https://arxiv.org/abs/1609.05091

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