Polar hypersurface

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

$f(x_0,x_1,x_2,\dots) = 0 \,$

and a point

$a = (a_0:a_1:a_2: \dots),$

its polar hypersurface P_a(C) is the hypersurface

$a_0 f_0 %2B a_1 f_1 %2B a_2 f_2%2B\cdots = 0, \,$

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