Class {$\rm VII\sb 0$} surfaces with {$b\sb 2$} curves

Abstract

We give an affirmative answer to the following conjecture of Ma, Kato: Let $S$ be a compact complex surface in Kodaira's class $\rm {VII_{0}}$ which contains a strictly positive number of rational curves being exactly equal to the second Betti number of $S$. Then $S$ admits a global spherical shell.