Quartic equations and 2-division on elliptic curves
| dc.creator | Hitching, George H. | |
| dc.date | 2007-06-29 | |
| dc.date.accessioned | 2026-07-07T08:13:07Z | |
| dc.date.available | 2026-07-07T08:13:07Z | |
| dc.description | Let K be a field of characteristic different from 2 and C an elliptic curve over K given by a Weierstrass equation. To divide an element of the group C by 2, one must solve a certain quartic equation. We characterise the quartics arising from this procedure and find how far the quartic determines the curve and the point. We find the quartics coming from 2-division of 2- and 3-torsion points, and generalise this correspondence to singular plane cubics. We use these results to study the question of which degree 4 maps of curves can be realised as duplication of a multisection on an elliptic surface. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0706.4379 | |
| dc.identifier | http://arxiv.org/abs/0706.4379 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132687 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H52; 14J27 | |
| dc.title | Quartic equations and 2-division on elliptic curves | |
| dc.type | text |