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Optimal bound for the number of \((-1)\)-curves on extremal rational surfaces. (English) Zbl 1043.14009

Summary: 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 has self-intersection zero. We also prove that a nonelliptic extremal rational surface has at most nine \((-1)\)-curves.

MSC:

14J26 Rational and ruled surfaces
14C20 Divisors, linear systems, invertible sheaves
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