For a generic genus 5 curve, the theta hyperplanes determine the set of enveloping quadrics, hence determine the curve; this yields a theta-hyperplane description of the Schottky locus in genus 5.
Coble, Algebraic geometry and Theta functions , revised printing, Amer
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Effective reconstruction of generic genus 5 curves from their theta hyperplanes
For a generic genus 5 curve, the theta hyperplanes determine the set of enveloping quadrics, hence determine the curve; this yields a theta-hyperplane description of the Schottky locus in genus 5.