Abstract
It was established by X. Mo and the author that the dimension of each irreducible component of the moduli space \mathcal{M}d, g(X) of branched superminimal immersions of degree d from a Riemann surface X of genus g into {C}P^3 lay between 2d-4g+4 and 2d-g+4 for d sufficiently large, where the upper bound was always assumed by the irreducible component of totally geodesic branched superminimal immersions and the lower bound was assumed by all nontotally geodesic irreducible components of \mathcal{M}6, 1(T) for any torus T. It is shown, via deformation theory, in this note that for d=8g+1+3k, k≥q 0, and any Riemann surface X of g≥q 1, the above lower bound is assumed by at least one irreducible component of \mathcal{M}d, g(X).
