= Gauss map of a theta divisor
{c}
{title2=$\Gamma:\Theta_{\mathrm{sm}}\to\mathbb P(T_0J^*)$}
Translate the tangent hyperplane at a smooth point of the <theta divisor> to the identity of the <Jacobian variety>. Its annihilator defines the Gauss map. At $L=\mathcal O_X(D)$ with $h^0(L)=1$, the <derivative of the Abelian sum map> identifies this annihilator with the unique line $H^0(K_X(-D))$. Thus $\Gamma(L)=[\omega]$ implies $D\le\operatorname{div}(\omega)$. This connects the intrinsic geometry of the <theta divisor> to the <canonical map> of the curve.
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