TY - JOUR

T1 - Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves

AU - Badr, Eslam

AU - Bars, Francesc

PY - 2019/1/1

Y1 - 2019/1/1

N2 - © 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.

AB - © 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.

KW - ELLIPTIC-CURVES

KW - Field of definition

KW - Field of moduli

KW - HYPERELLIPTIC CURVES

KW - Smooth plane curves

UR - http://www.mendeley.com/research/plane-modelfields-definition-fields-definition-field-moduli-smooth-plane-curves

U2 - https://doi.org/10.1016/j.jnt.2018.07.010

DO - https://doi.org/10.1016/j.jnt.2018.07.010

M3 - Article

VL - 194

SP - 278

EP - 283

ER -