Complutense University Library

A note on projections of real algebraic varieties.

Andradas Heranz, Carlos and Gamboa Mutuberria, José Manuel (1984) A note on projections of real algebraic varieties. Pacific Journal of Mathematics, 115 . pp. 1-11. ISSN 0030-8730

[img] PDF
Restricted to Repository staff only until 2020.

866kB

Official URL: http://projecteuclid.org/pjm

View download statistics for this eprint

==>>> Export to other formats

Abstract

We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some Rn + k. We apply this result to show that any clopen subset of the space of orders of the field of rational functions K= R(X1,...iXn) is the image of the space of orders of a finite extension of K.


Item Type:Article
Uncontrolled Keywords:Real algebraic varieties; Regularly closed semialgebraic set; Clopen subset; Space of orders of rational functions
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14843
References:

G. W. Brumfiel, Partially ordered fields and semialgebraic geometry, London Math. Soc. Lect. Notes, 37 (1979).

M. Coste and M. F. Roy, La topologie du spectre reel, Contemporary Math., 8 (1982), 27-59.

D. W. Dubois and T. Recio, Order extensions and real algebraic geometric, Contemporary Math., 8 (1982), 265-288.

R. Elman, T. Y. Lam and A. Wadsworth, Orderings under field extensions, J. Reine Ang. Math., 306 (1979), 7-27.

R. Hartshorne, Algebraic Geometry, G.T.M. no. 52, Springer Verlag, (1977).

T. S. Motzkin, The Real Solution Set of a System of Algebraic Inequalities, Inequalities II, Academic Press (1970).

A. Prestel, Lectures on Formally Real Fields, I.M.P.A. no. 25, (1975).

T. Recio, Una descomposicibn de un conjunto semialgebraico, Actas V Congreso de Matematicas de expresiόn Latina. Mallorca, Spain, (1977).

Deposited On:18 Apr 2012 10:29
Last Modified:06 Feb 2014 10:10

Repository Staff Only: item control page