International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 44, Pages 2803-2827
doi:10.1155/S0161171203112161
On the moduli space of superminimal surfaces in spheres
Departamento de Matemáticas, Universidad de los Andes, Apartado Aereo, Bogotá 4976, Colombia
Received 25 December 2001
Copyright © 2003 Luis Fernández. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Using a birational correspondence between the twistor space of S2n and projective space, we describe, up to birational equivalence, the moduli space of superminimal surfaces in S2n of degree d as curves of degree d in projective space satisfying a certain differential system. Using this approach, we show that the moduli space of linearly full maps is nonempty for sufficiently large degree and we show that the dimension of this moduli space for n=3 and genus 0 is greater than or equal to 2d+9. We also give a direct, simple proof of the connectedness of the moduli space of superminimal surfaces in S2n of degree d.