Polar hypersurface - Alchetron, The Free Social Encyclopedia

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

f ( x 0 , x 1 , x 2 , … ) = 0

and a point

a = ( a 0 : a 1 : a 2 : … ) ,

its polar hypersurface P_a(C) is the hypersurface

a 0 f 0 + a 1 f 1 + a 2 f 2 + ⋯ = 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.

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