Field of moduli and field of definition for curves of genus 2 Gabriel Cardona
نویسندگان
چکیده
Let M2 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] ∈ M2 is defined over k. In [7], Mestre solves the converse problem for curves with Aut(C) ≃ C2. 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 Br2(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.
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