On the moduli space of superminimal surfaces in spheres
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...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203112161 |
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| _version_ | 1832554548593426432 |
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| author | Luis Fernández |
| author_facet | Luis Fernández |
| author_sort | Luis Fernández |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2028266fcd844de2adbf0b9fb08a42eb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2028266fcd844de2adbf0b9fb08a42eb2025-02-03T05:51:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003442803282710.1155/S0161171203112161On the moduli space of superminimal surfaces in spheresLuis Fernández0Departamento de Matemáticas, Universidad de los Andes, Apartado Aereo, Bogotá 4976, ColombiaUsing 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.http://dx.doi.org/10.1155/S0161171203112161 |
| spellingShingle | Luis Fernández On the moduli space of superminimal surfaces in spheres International Journal of Mathematics and Mathematical Sciences |
| title | On the moduli space of superminimal surfaces in spheres |
| title_full | On the moduli space of superminimal surfaces in spheres |
| title_fullStr | On the moduli space of superminimal surfaces in spheres |
| title_full_unstemmed | On the moduli space of superminimal surfaces in spheres |
| title_short | On the moduli space of superminimal surfaces in spheres |
| title_sort | on the moduli space of superminimal surfaces in spheres |
| url | http://dx.doi.org/10.1155/S0161171203112161 |
| work_keys_str_mv | AT luisfernandez onthemodulispaceofsuperminimalsurfacesinspheres |