International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 2, Pages 123-126
doi:10.1155/S0161171202013194

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

Abstract

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.