Impacto
Downloads
Downloads per month over past year
Gamboa, J. M. (1984) A Characterization Of Rational And Elliptic Real AlgebraicCurves In Terms Of Their Space Of Orderings. Rocky Mountain Journal Of Mathematics, 14 (3). pp. 499502. ISSN 00357596

PDF
100kB 
Official URL: http://rmmc.eas.asu.edu/rmj/rmj.html
URL  URL Type 

http://projecteuclid.org  Organisation 
Abstract
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, 265288 (1982; Zbl 0484.12003) under the name of Q1fields. They were further studied by the author and T. Recio [J. Pure Appl.
Algebra 30, 237246 (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.
Item Type:  Article 

Uncontrolled Keywords:  rational curve; formally real field; space of orderings; dense orbits property; Q1fields; function fields of real algebraic varieties; elliptic curve 
Subjects:  Sciences > Mathematics > Algebraic geometry 
ID Code:  15388 
Deposited On:  28 May 2012 08:59 
Last Modified:  22 Aug 2018 10:19 
Origin of downloads
Repository Staff Only: item control page