Polar hypersurface

In algebraic geometry, given a projective algebraic hypersurface C described by the homogeneous equation

${\displaystyle f(x_{0},x_{1},x_{2},\dots )=0\,}$

and a point

${\displaystyle a=(a_{0}:a_{1}:a_{2}:\dots ),}$

its polar hypersurface P_a(C) is the hypersurface

${\displaystyle a_{0}f_{0}+a_{1}f_{1}+a_{2}f_{2}+\cdots =0,\,}$

where ƒ_i are the partial derivatives.

The intersection of C and P_a(C) is the set of points p such that the tangent at p to C meets a.

References

• Dolgachev, Igor, Topics in classical algebraic geometry