Non Kählerian surfaces with a cycle of rational curves

Abstract Let S be a compact complex surface in class VII 0 + containing cycle of rational curves C = ∑ D j . A the maximal connected divisor If there is another component ′ then curves, and Inoue-Hirzebruch surface. only one each i chain which intersects curve for at most meets In other words, we do not prove existence those , but if some exist looks like Kato with perhaps missing curves. The proof this topological result an application Donaldson theorem on trivialization intersection form deformation theory. We apply to show that twisted logarithmic 1-form has trivial vanishing divisor.