Introduction

  • Jacek Bochnak
  • Michel Coste
  • Marie-Françoise Roy
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 36)

Abstract

In simplest terms, algebraic geometry is the study of the set of solutions of a system of polynomial equations. The main goal of real algebraic geometry is the study of real algebraic sets i.e. subsets of n defined by polynomial equations. By means of a simple example one can see some features which point up the difference between real and complex algebraic geometry. Let us consider the intersection of the straight line x = t, depending on the parameter t, with the cubic y 2 = x 3 - x. For t = -1,0,1 the straight line is tangent to the cubic. In the complex plane, when t is different from -1,0,1, the straight line always intersects the cubic in two points. In the real plane the situation is more intricate.

Keywords

Manifold Coherence Stratification Nash 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jacek Bochnak
    • 1
  • Michel Coste
    • 2
  • Marie-Françoise Roy
    • 1
  1. 1.Mathematisch InstituutVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Institut Mathématique de RennesUniversité de Rennes 1Rennes cedexFrance

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