Igusa quartic explained

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 .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

\sum x _{i=0} ( \sum x ^{2 )} _{i} ^{2} = 4 \sum x ^{4} _{i}