Moduli space of branched superminimal immersions of a compact Riemann surface into S4

Abstract

In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max{2g, g + 2}, such spaces have the structure of projectivized fibre products and are path-connected quasi-projective varieties of dimension 2d - g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.