Superminimal surfaces in the 6-sphere

In this article, we use the harmonic sequence associated to a weakly conformal harmonic map f: S → S ⁶ in order to determine explicit examples of linearly full almost complex 2-spheres of S ⁶ with at most two singularities. We prove that the singularity type of these almost complex 2-spheres has an extra symmetry and this allows us to determine the moduli space of such curves with suitably small area. We also characterize projectively equivalent almost complex curves of S ⁶ in terms of G ₂ ^? -equivalence of their directrix curves.