CLASS $\\textrm{VII}_0$ SURFACES WITH $b_2$ 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 $\textrm{VII}_0$ 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.