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

Eslam Badr, Francesc Bars

Research output: Contribution to journalArticleResearch

Abstract

© 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.
Original languageEnglish
Pages (from-to)278-283
JournalJournal of Number Theory
Volume194
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Field of definition
  • Field of moduli
  • Smooth plane curves

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