Optimal bound for the number of (−1)-curves on extremal rational surfaces
We give an optimal bound for the number of (−1)-curves on an extremal rational surface X under the assumption that −KX is numerically effective and having self-intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine (−1)-curves.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013194 |
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| _version_ | 1850178376069808128 |
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| author | Mustapha Lahyane |
| author_facet | Mustapha Lahyane |
| author_sort | Mustapha Lahyane |
| collection | DOAJ |
| description | We give an optimal bound for the number of (−1)-curves on an extremal rational surface X under the assumption that −KX is numerically effective and having self-intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine (−1)-curves. |
| format | Article |
| id | doaj-art-c4a53771db2a4ff288b7719174bd3f2b |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c4a53771db2a4ff288b7719174bd3f2b2025-08-20T02:18:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131212312610.1155/S0161171202013194Optimal bound for the number of (−1)-curves on extremal rational surfacesMustapha Lahyane0Abdus Salam International Centre for Theoretical Physics, Trieste 34100, ItalyWe give an optimal bound for the number of (−1)-curves on an extremal rational surface X under the assumption that −KX is numerically effective and having self-intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine (−1)-curves.http://dx.doi.org/10.1155/S0161171202013194 |
| spellingShingle | Mustapha Lahyane Optimal bound for the number of (−1)-curves on extremal rational surfaces International Journal of Mathematics and Mathematical Sciences |
| title | Optimal bound for the number of (−1)-curves on extremal rational surfaces |
| title_full | Optimal bound for the number of (−1)-curves on extremal rational surfaces |
| title_fullStr | Optimal bound for the number of (−1)-curves on extremal rational surfaces |
| title_full_unstemmed | Optimal bound for the number of (−1)-curves on extremal rational surfaces |
| title_short | Optimal bound for the number of (−1)-curves on extremal rational surfaces |
| title_sort | optimal bound for the number of 1 curves on extremal rational surfaces |
| url | http://dx.doi.org/10.1155/S0161171202013194 |
| work_keys_str_mv | AT mustaphalahyane optimalboundforthenumberof1curvesonextremalrationalsurfaces |