The arithmetic of Prym varieties in genus 3
| dc.creator | Bruin, Nils | |
| dc.date | 2004-08-04 | |
| dc.date | 2006-05-31 | |
| dc.date.accessioned | 2026-07-07T10:11:50Z | |
| dc.date.available | 2026-07-07T10:11:50Z | |
| dc.description | Given a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym-variety. We also describe how an unramified double cover of a non-hyperelliptic genus 3 curve can be mapped into the Jacobian of a curve of genus 2 over its field of definition and how this can be used to do Chabauty- and Brauer-Manin type calculations for curves of genus 5 with an unramified involution. As an application, we determine the rational points on a smooth plane quartic with no particular geometric properties and give examples of curves of genus 3 and 5 violating the Hasse-principle. We also show how these constructions can be used to design smooth plane quartics with specific arithmetic properties. As an example, we give a smooth plane quartic with all 28 bitangents defined over Q(t). | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408069 | |
| dc.identifier | http://arxiv.org/abs/math/0408069 | |
| dc.identifier | Compos. Math. 144 (2008), no. 2, 317--338. | |
| dc.identifier | doi:10.1112/S0010437X07003314 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171989 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G30; 14H40 | |
| dc.title | The arithmetic of Prym varieties in genus 3 | |
| dc.type | text |