Abstract
AnH 2,2-invariant quartic surface in ℙ3 is a quartic surface in ℙ3 invariant under the Heisenberg groupH 2,2 of level (2, 2), the family ofH 2,2-invariant quartic surfaces is parametrized by ℙ4. For each ν ε ℙ4, the corresponding quartic surfaceX ν will be a Kummer surface, ifX ν is singular. The equation for {Δ = 0} ⊂ ℙ4 parametrizing all Kummer surfaces is well known. We find another more symmetric form (with respect to a 5-dimensional representation of the symmetric group S6) for this equation.
The aim of this note is to describe all singularH 2,2-invariant quartic surfaces in ℙ3.
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