Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves
| Autor: | Eslam Badr, Francesc Bars |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Plane (geometry) Plane curve 010102 general mathematics Field (mathematics) 010103 numerical & computational mathematics Field of definition 01 natural sciences Algebraic closure Field of moduli Moduli Perfect field Smooth plane curves 0101 mathematics Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2018.07.010 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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