On surfaces of class \(VII_ 0\) with curves. II (Q5903380)

[For part I see ibid. 58, 380-383 (1982; Zbl 0519.32017); see also Invent. Math. 78, 393-443 (1984; Zbl 0575.14033).] Theorem: Let S be a \(VII_ 0\) surface with a cycle of rational curves C. Then there exist a proper family \(\pi: {\mathcal S}\to \Delta\) where \(\Delta\) is an open unit disc and a \(\pi\)-flat Cartier divisor \({\mathcal C}\) such that (\({\mathcal S}_ 0,{\mathcal C}_ 0)\overset \sim \rightarrow (S,C)\). If \(t\neq 0\), then \({\mathcal S}_ t\) is a blown up primary Hopf surface with a non singular elliptic curve \({\mathcal C}_ t\). Furthermore, the weighted dual graph of all the curves on surfaces S with \(b_ 2\) rational curves is determined. From this, the author gives a characterization of half-Inoue surfaces.