A note on projections of real algebraic varieties

Carlos Andradas Heranz and José Manuel Gamboa Mutuberría

Vol. 115 (1984), No. 1, 1–11

DOI: 10.2140/pjm.1984.115.1

Abstract

We prove that any regularly closed semialgebraic set of Rⁿ, 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 R^n+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,…,X_n) is the image of the space of orders of a finite extension of K.

Mathematical Subject Classification 2000

Primary: 12D15

Secondary: 14A10, 14G30

Milestones

Received: 20 January 1983

Published: 1 November 1984