Families of elliptic curves with genus 2 covers of degree 2
| dc.creator | Diem, Claus | |
| dc.date | 2003-12-22 | |
| dc.date | 2006-05-17 | |
| dc.date.accessioned | 2026-07-07T06:35:53Z | |
| dc.date.available | 2026-07-07T06:35:53Z | |
| dc.description | We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of relative elliptic curves determine the cover in a unique way (up to isomorphism). A classical theorem says that a genus 2 cover of an elliptic curve of degree 2 over a field of characteristic different from 2 is birational to a product of two elliptic curves over the projective line. We formulate and prove a generalization of this theorem for the relative situation. We also prove a Torelli theorem for genus 2 curves over an arbitrary base. | |
| dc.description | 27 pages; final version | |
| dc.identifier | https://arxiv.org/abs/math/0312413 | |
| dc.identifier | http://arxiv.org/abs/math/0312413 | |
| dc.identifier | Collect.Math. 57, 1 (2006) 1-25 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99930 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H45 | |
| dc.title | Families of elliptic curves with genus 2 covers of degree 2 | |
| dc.type | text |