Surfaces with many nodes

Abstract

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the second Betti number. In the last section this is applied to the study of minimal complex surfaces of general type with $p_g=0$ and $K^2=8,9$ which admit an automorphism of order 2.

Latex 2e, 17 pages