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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Main Author: Mustapha Lahyane
Format: Article
Language:English
Published: Wiley 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202013194
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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.
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1687-0425
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publishDate 2002-01-01
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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