In algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quarticCR4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic hypersurface in 4-dimensional projective space, studied by Igusa (1962).
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
represented as a double cover of the projective 4-space branched over the Igusaquartic. It is a 4-dimensional variety that was first studied by Arthur Coble...
hyperplane xi = xj is Cayley's nodal cubic surface. Its dual is the Igusaquartic 3-fold in P4. Its Hessian is the Barth–Nieto quintic. A cubic hypersurface...
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