Polars of Real Singular Plane Curves
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 wordsPolar varieties hypersurfaces plane curves tangent space flag
AMS(MOS) subject classificationsPrimary 14H50 Secondary 14J70 14P05 14Q05
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- S. ENDRASS et al. Surf 1.0.4. 2003. A Computer Software for Visualising Real Algebraic Geometry, http://surf.sourceforge.net.Google Scholar
- M. SAFEY EL DIN. Putting into practice deformation techniques for the computation of sampling points in real singular hypersurfaces. 2005.Google Scholar
- M. SAFEY EL DIN AND E. SCHOST. Polar varieties and computation of one point in each connected component of a smooth algebraic set. In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 224–231 (electronic), New York, 2003. ACM.Google Scholar