© 2018 Elsevier Inc. 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.
|Number of pages||6|
|Journal||Journal of Number Theory|
|Publication status||Published - 1 Jan 2019|
- Field of definition
- Field of moduli
- HYPERELLIPTIC CURVES
- Smooth plane curves