If such a complex structure exists, it would weird indeed! For example, as shown by Campana, Demaily and Peternell (Compositio 112, 77-91), if such a thing exists, then $S^6$ would have no meromorphic functions. In particular, $S^6$ can't be Moishezon, let alone algebraic.

If such a complex structure exists, it would weird indeed! For example, as shown by Campana, Demailly and Peternell (Compositio 112, 77-91), if such a thing exists, then $S^6$ would have no non-constant meromorphic functions. In particular, $S^6$ can't be Moishezon, let alone algebraic.