Field of moduli and field of definition for curves of genus 2
| dc.creator | Cardona, Gabriel | |
| dc.creator | Quer, Jordi | |
| dc.date | 2002-07-02 | |
| dc.date.accessioned | 2026-07-07T04:49:29Z | |
| dc.date.available | 2026-07-07T04:49:29Z | |
| dc.description | Let M_2 be the moduli space that classifies genus 2 curves. If a curve C is defined over a field k, the corresponding moduli point P=[C] is defined over k. Mestre solved the converse problem for curves with Aut(C) isomorphic to C_2. Given a moduli point defined over k, Mestre finds an obstruction to the existence of a corresponding curve defined over k, that is an element in Br_2(k) not always trivial. In this paper we prove that for all the other possibilities of Aut(C), every moduli point defined over k is represented by a curve defined over k. We also give an explicit construction of such a curve in terms of the coordinates of the moduli point. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207015 | |
| dc.identifier | http://arxiv.org/abs/math/0207015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64440 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Field of moduli and field of definition for curves of genus 2 | |
| dc.type | text |