Uniformity of quadratic points
Tangli Ge
TL;DR
This paper extends a uniformity result to dimension two and establishes a bound on quadratic points for certain curves based on their Mordell-Weil rank.
Contribution
It generalizes a known uniformity result to higher dimension and provides a new bound on quadratic points for specific algebraic curves.
Findings
Extended uniformity result to dimension two.
Established a bound on quadratic points in terms of Mordell-Weil rank.
Applicable to non-hyperelliptic, non-bielliptic curves.
Abstract
In this paper, we extend a uniformity result of Dimitrov-Gao-Habegger to dimension two and use it to get a uniform bound on the set of all quadratic points for non-hyperelliptic non-bielliptic curves in terms of the Mordell-Weil rank.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic and geometric function theory · Nonlinear Partial Differential Equations