Mathematische Zeitschrift

, Volume 239, Issue 1, pp 131–142 | Cite as

The complexification and degree of a semi-algebraic set

  • Marie-Françoise Roy
  • Nicolai Vorobjov
Original article


The complexification of a semi-algebraic set \(S \subset{\bf R}^n\) is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than \(s^nO(d)^{2n}\).


Geometric Degree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marie-Françoise Roy
    • 1
  • Nicolai Vorobjov
    • 2
  1. 1.IRMAR (UMR CNRS 6625), Université de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, FranceFR
  2. 2.Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UKGB

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