English

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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