Examples of effectivity for integral points on certain curves of genus 2
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913628543778816 |
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| author | Corvaja, Pietro Lombardo, Davide Zannier, Umberto |
| author_facet | Corvaja, Pietro Lombardo, Davide Zannier, Umberto |
| contents | 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 étale covers of such curves of genus 2 and the study of the torsion values of sections of certain doubly elliptic abelian schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Examples of effectivity for integral points on certain curves of genus 2 Corvaja, Pietro Lombardo, Davide Zannier, Umberto Number Theory Algebraic Geometry 11D99, 11G30, 14G05 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 étale covers of such curves of genus 2 and the study of the torsion values of sections of certain doubly elliptic abelian schemes. |
| title | Examples of effectivity for integral points on certain curves of genus 2 |
| topic | Number Theory Algebraic Geometry 11D99, 11G30, 14G05 |
| url | https://arxiv.org/abs/2411.17930 |