= Projective dual variety
{title2=$Y^*\subset\mathbb P(V^*)$}
For an irreducible <projective variety> $Y\subset\mathbb P(V)$, its projective dual is the closure of hyperplanes containing the embedded tangent space at some smooth point of $Y$. Over the <complex numbers>, biduality gives $(Y^*)^*=Y$. For a nondegenerate smooth curve in characteristic zero, the dual is an irreducible hypersurface; a general point corresponds to one ordinary tangency. Its defining incidence space consists of a point on the curve and a hyperplane containing its tangent line.
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