| Título: | A Characterization Of Rational And Elliptic Real Algebraic-Curves In Terms Of Their Space Of Orderings |
| Autores: | Gamboa, J. M. |
| Tipo de documento: | texto impreso |
| Editorial: | Rocky Mountain Journal Of Mathematics, 1984 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometria algebraica , Tipo = Artículo |
| Resumen: |
Let K be a formally real field with space of orderings X(K). Then Aut(K) operates on X(K). K is said to have the ”dense orbits property” if for any x 2 X(K) the orbit of x is dense in X(K). Fields with the dense orbits property were introduced by D. W. Dubois and T. Recio in Contemp. Math. 8, 265-288 (1982; Zbl 0484.12003) under the name of Q1-fields. They were further studied by the author and T. Recio [J. Pure Appl. Algebra 30, 237-246 (1983; Zbl 0533.12018)]. In the present paper the dense orbits property is studied for function fields of real algebraic varieties. So, let V be a real algebraic variety over the field R of real numbers, R(V ) the function field of V. It is proved that Aut(R(V )) is infinite if R(V ) has the dense orbits property. If V is a curve then R(V ) has the dense orbits property if and only if V is a rational or elliptic curve. |
| En línea: | https://eprints.ucm.es/id/eprint/15388/1/42.pdf |
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