Coble hypersurface

In algebraic geometry, a Coble hypersurface is one of the hypersurfaces associated to the Jacobian variety of a curve of genus 2 or 3 by Arthur Coble.

There are two similar but different types of Coble hypersurfaces.
 * The Kummer variety of the Jacobian of a genus 3 curve can be embedded in 7-dimensional projective space under the 2-theta map, and is  then the singular locus of a  6-dimensional quartic hypersurface, called a Coble hypersurface.
 * Similarly the Jacobian of a genus 2 curve can be embedded in 8-dimensional projective space under the 3-theta map, and is then the singular locus of a  7-dimensional cubic hypersurface, also called a Coble hypersurface.