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Central orderings in fields of real meromorphic function germs

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Ruiz Sancho, Jesús María (1984) Central orderings in fields of real meromorphic function germs. Manuscripta mathematica, 46 (1-3). pp. 193-214. ISSN 0025-2611

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Abstract

The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0⊂Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the closure of the set of smooth points of maximal dimension). In the case of germs, the central points are replaced by curves or, more precisely, half branch germs (actually even C∞ branch germs); the dimension of a half branch germ is the dimension of the smallest analytic germ which contains this half germ. An order on K(X0) is said to be centered on a half branch c if the set of its positive elements contains the functions which are positive on c. If Ωe is the set of orders on K(X0) centered on a half branch of dimension e, it is proved that all Ωe (e=1,⋯,d) and Ω∖Ω∗ (with Ω∗=Ω1∪⋯∪Ωd) are dense in Ω. Various other results and applications are given.


Item Type:Article
Uncontrolled Keywords:Analytic germ; semi-analytic real spectrum; space of orders of the field of germs of meromorphic functions; formal half branch; maximum dimension locus; Hilbert 17th problem
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:20346
Deposited On:08 Mar 2013 17:11
Last Modified:12 Dec 2018 15:14

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