RT Journal Article
T1 On Orderings In Real Surfaces
A1 Gamboa Mutuberria, José Manuel
A1 Alonso García, María Emilia
A1 Ruiz Sancho, Jesús María
AB 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 < t such that fw is defined and positive on (0,t). In the present paper it is shown that the total orderings of the function field of an algebraic surface over thefield 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 < t 2 R.
PB Elsevier Science B.V. (North-Holland)
SN 0022-4049
YR 1985
FD 1985
LK https://hdl.handle.net/20.500.14352/64630
UL https://hdl.handle.net/20.500.14352/64630
DS Docta Complutense
RD 5 abr 2025