Título: | On Orderings In Real Surfaces |
Autores: | Gamboa, J. M. ; Alonso García, María Emilia ; Ruiz Sancho, Jesús María |
Tipo de documento: | texto impreso |
Editorial: | Elsevier Science B.V. (North-Holland), 1985 |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometria algebraica , Tipo = Artículo |
Resumen: |
It is well-known that if C is an algebraic curve over the real closed field R and is a total ordering of the function field R(C) of C then there is a semi-algebraic embedding w : (0, 1) ! C such that f 2 R(C) is positive with respect to if and only if there is some t 2 R, 0
In the present paper it is shown that the total orderings of the function field of an algebraic surface over the field R of real numbers admits a similar geometric description. Let V be an irreducible algebraic surface over R embedded in some Rn. Using a discussion of the orderings of the meromorphic function germs of an irreducible analytic surface germ the following is proved: If is a total ordering of R(V ) then there is an analytic map c : (0, 1) ! V such that f 2 R(V ) is positive with respect to if and only if fc is defined and positive on (0,t) for some 0 |
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