Examples of effectivity for integral points on certain curves of genus 2
Number Theory
2024-12-31 v2 Algebraic Geometry
Abstract
We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively determined. Our method is based on the construction of degree-3 \'etale covers of such curves of genus 2 and the study of the torsion values of sections of certain doubly elliptic abelian schemes.
Keywords
Cite
@article{arxiv.2411.17930,
title = {Examples of effectivity for integral points on certain curves of genus 2},
author = {Pietro Corvaja and Davide Lombardo and Umberto Zannier},
journal= {arXiv preprint arXiv:2411.17930},
year = {2024}
}
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