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

$a=(a_0:a_1:a_2:\cdots )$

its polar hypersurface $P_a(C)$ is the hypersurface

$a_0{f}_0+a_1{f}_1+a_2{f}_2+\cdots =0,$

where $f_i$ are the partial derivatives of $f$.

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

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