= Projective biduality theorem
{title2=$(Y^*)^*=Y$}
Over the <complex numbers>, an irreducible <projective variety> is recovered by applying <projective dual variety> twice. In its conormal incidence variety, pairs $(y,H)$ with $H$ tangent at $y$ become pairs $(H,y)$ under exchange of the two projective factors. At general smooth pairs, differentiating the incidence equation shows that the hyperplane defined by $y$ is tangent to the dual variety at $H$. Closure gives the same conormal variety with the factors exchanged, proving biduality. This is why the branch hypersurface of the <Gauss map of a theta divisor> determines a nonhyperelliptic canonical curve.
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