Non-thin rank jumps for double elliptic K3 surfaces
| dc.contributor.author | Pasten, Hector | |
| dc.contributor.author | Salgado, Cecilia | |
| dc.date.accessioned | 2025-01-20T16:14:29Z | |
| dc.date.available | 2025-01-20T16:14:29Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | For an elliptic surface pi:X -> P1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi :X\rightarrow \mathbb {P}<^>1$$\end{document} defined over a number field K, a theorem of Silverman shows that for all but finitely many fibres above K-rational points, the resulting elliptic curve over K has Mordell-Weil rank at least as large as the rank of the group of sections of pi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}. When X is a K3 surface with two distinct elliptic fibrations, we show that the set of K-rational points of P1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}<^>1$$\end{document} for which this rank inequality is strict, is not a thin set, under certain hypothesis on the fibrations. Our results provide one of the first cases of this phenomenon beyond that of rational elliptic surfaces. | |
| dc.fuente.origen | WOS | |
| dc.identifier.doi | 10.1007/s00229-024-01554-2 | |
| dc.identifier.eissn | 1432-1785 | |
| dc.identifier.issn | 0025-2611 | |
| dc.identifier.uri | https://doi.org/10.1007/s00229-024-01554-2 | |
| dc.identifier.uri | https://repositorio.uc.cl/handle/11534/90443 | |
| dc.identifier.wosid | WOS:001257451700001 | |
| dc.issue.numero | 3-4 | |
| dc.language.iso | en | |
| dc.pagina.final | 781 | |
| dc.pagina.inicio | 771 | |
| dc.revista | Manuscripta mathematica | |
| dc.rights | acceso restringido | |
| dc.subject | Primary 14J27 | |
| dc.subject | 14J28 | |
| dc.subject | Secondary 11G05 | |
| dc.subject | 14D10 | |
| dc.title | Non-thin rank jumps for double elliptic K3 surfaces | |
| dc.type | artículo | |
| dc.volumen | 175 | |
| sipa.index | WOS | |
| sipa.trazabilidad | WOS;2025-01-12 |