Igusa quartic

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 Template:Harvs. 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

$\sum x_i=0$

$(\sum x_i^2{)}^2=4\sum x_i^4$

References

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