On the compactification of the moduli space of branched minimal immersions of S2 into S4

We study the natural compactification of the moduli space of branched minimal immersions of S2 into S4. We prove that the (compactified) moduli space Md is a connected projective variety of dimension 2d+4. It is irreducible when d=1,2, and it has two irreducible components when d ≥ 3. We discuss the bubbling phenomenon at the boundary of the moduli space. (author). 26 refs, 3 figs