Geodesic
THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES
Forum of Mathematics, Sigma, Tome 7 (2019)

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In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are small enough to successfully implement a computer search. As an evidence of the simplicity of its application, we present a variety of explicit examples and explain how to produce many others. In the appendix our method is compared in detail to the classical method of Manin–Demjanenko and the analysis of our explicit examples is carried to conclusion. 
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     author = {SARA CHECCOLI and FRANCESCO VENEZIANO and EVELINA VIADA},
     title = {THE {EXPLICIT} {MORDELL} {CONJECTURE} {FOR} {FAMILIES} {OF} {CURVES}},
     journal = {Forum of Mathematics, Sigma},
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SARA CHECCOLI; FRANCESCO VENEZIANO; EVELINA VIADA. THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.20

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