Let C/k‾ be a smooth plane curve defined over k‾ a fixed algebraic closure of a perfect field k. We call a subfield k′⊆k‾ a plane model-field of definition for C if C descends to k′ as a smooth plane curve over k′, that is if there exists a smooth curve C′/k′ defined over k′ which is k′-isomorphic to a non-singular plane model F(X,Y,Z)=0 with coefficients in k′, and such that C′⊗k′k‾ and C are isomorphic. In this paper, we provide (explicit) families of smooth plane curves for which the three fields types; the field of moduli, fields of definition, and plane-models fields of definition are pairwise different.
CITATION STYLE
Badr, E., & Bars, F. (2019). Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves. Journal of Number Theory, 194, 278–283. https://doi.org/10.1016/j.jnt.2018.07.010
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