algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, given a projective algebraic

hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidean ...

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 + 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

*{{citation, authorlink=Igor Dolgachev, last=Dolgachev, first=Igor, url=http://www.math.lsa.umich.edu/~idolga/lecturenotes.html, title=Topics in classical algebraic geometry Projective geometry