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27 pagesWe give an affirmative answer to a conjecture of Ma. Kato, namely that every compact complex surface $S$ in Kodaira's class $VII_0$ with $b_2(S) > 0$ and $b_2(S)$ rational curves, admits a global spherical shell

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