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Optimal bound for the number of ( − 1 ) -curves on extremal rational surfaces

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  • Mustapha Lahyane

Abstract

We give an optimal bound for the number of ( − 1 ) -curves on an extremal rational surface X under the assumption that − K X is numerically effective and having self-intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine ( − 1 ) -curves.

Suggested Citation

  • Mustapha Lahyane, 2002. "Optimal bound for the number of ( − 1 ) -curves on extremal rational surfaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:151052
    DOI: 10.1155/S0161171202013194
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