The space of almost complex 2-spheres in the 6-sphere

The complex dimension of the space of linearly full almost complex 2-spheres of area 4 π d 4\pi d in the round 6-sphere is calculated to be d + 8 d+8 . Explicit examples of these objects are constructed for every integer value of the degree, d ≥ 6 d\ge 6 , d ≠ 7 d\ne 7 . Furthermore, it is shown that when d = 6 d=6 this space is isomorphic to the group G 2 ( C ) G_2({\mathbb C}) , and when d = 7 d=7 this space is empty. We also show that the dimension of the space of nonlinearly full almost complex 2-spheres of area 4 π d 4\pi d in the round 6-sphere is 2 d + 5 2d+5 .