In algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quartic CR4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic hypersurface in 4-dimensional projective space, studied by Igusa.It is closely related to the moduli space of genus 2 curves with level 2 structure. It is the dual of the Segre cubic. It can be given as a codimension 2 variety in P5 by the equations
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