Moduli space of branched superminimal immersions of a compact Riemann surface into S 4

@article{Loo1999ModuliSO,
  title={Moduli space of branched superminimal immersions of a compact Riemann surface into S 4},
  author={B. Loo},
  journal={Journal of The Australian Mathematical Society},
  year={1999},
  volume={66},
  pages={32-50}
}
  • B. Loo
  • Published 1999
  • Mathematics
  • Journal of The Australian Mathematical Society
In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S 4 . We prove that when d ≥ max {2 g , g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2 d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S 4 . 
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