Polars of Real Singular Plane Curves

  • Heidi Camilla Mork
  • Ragni Piene
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 146)


Polar varieties have in recent years been used by Bank, Giusti, Heintz, Mbakop, and Pardo, and by Safey El Din and Schost, to find efficient procedures for determining points on all real components of a given non-singular algebraic variety. In this note we review the classical notion of polars and polar varieties, as well as the construction of what we here call reciprocal polar varieties. In particular we consider the case of real affine plane curves, and we give conditions for when the polar varieties of singular curves contain points on all real components.

Key words

Polar varieties hypersurfaces plane curves tangent space flag 

AMS(MOS) subject classifications

Primary 14H50 Secondary 14J70 14P05 14Q05 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Heidi Camilla Mork
    • 1
  • Ragni Piene
    • 1
  1. 1.CMA, Department of MathematicsUniversity of OsloOsloNorway

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