In
algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quartic ''CR''
4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic
hypersurface
In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidea ...
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 In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 (or sometimes 5) dimensional projective space, studied by .
Definition
The Segre cubic is the set of points (''x''0:''x''1:''x''2:''x''3:''x''4:''x''5) of ''P''5 satisfyin ...
.
It can be given as a codimension 2 variety in ''P''
5 by the equations
:
:
References
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*
*
3-folds
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