K3 surfaces, rational curves, and rational points
| dc.creator | Baragar, Arthur | |
| dc.creator | McKinnon, David | |
| dc.date | 2007-09-05 | |
| dc.date | 2008-07-20 | |
| dc.date.accessioned | 2026-07-07T09:51:28Z | |
| dc.date.available | 2026-07-07T09:51:28Z | |
| dc.description | We prove that for any of a wide class of elliptic surfaces $X$ defined over a number field $k$, if there is an algebraic point on $X$ that lies on only finitely many rational curves, then there is an algebraic point on $X$ that lies on no rational curves. In particular, our theorem applies to a large class of elliptic $K3$ surfaces, which relates to a question posed by Bogomolov in 1981. We apply our results to construct an explicit algebraic point on a $K3$ surface that does not lie on any smooth rational curves. | |
| dc.description | 10 pages, no figures. An explicit construction of an algebraic point lying on no smooth rational curves has been added to the end, and there have been minor revisions to the rest of the paper | |
| dc.identifier | https://arxiv.org/abs/0709.0663 | |
| dc.identifier | http://arxiv.org/abs/0709.0663 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165263 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G05 | |
| dc.title | K3 surfaces, rational curves, and rational points | |
| dc.type | text |