Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:240664 |
| Acceso en línea: | https://ddd.uab.cat/record/240664 https://dx.doi.org/urn:doi:10.1016/j.jnt.2018.07.010 |
| Access Level: | acceso abierto |
| Palabra clave: | Smooth plane curves Field of moduli Field of definition |
| Sumario: | 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. |
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