= Branch locus of the theta Gauss map
{title2=$B\subset\mathbb P(T_0J^*)$}
Normalize the target in the <function field> of the generically finite <Gauss map of a theta divisor>; its finite map has an intrinsic branch locus. For a nonhyperelliptic <smooth projective curve>, this locus is the <projective dual variety> of the canonical curve. For a <hyperelliptic curve> of genus at least three, it is the union of the dual hypersurface of its canonical <rational normal curve> and the $2g+2$ hyperplanes corresponding to branch points. Locally, ramification exchanges two roots of a hyperplane section, or exchanges the two lifts of a root passing through a branch point. Biduality then recovers the curve or its double-cover data.
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