Canonical bundles of compact complex surfaces containing global spherical shells (Q1096683)

The author determines numerically (i.e. in \(H^ 2(S,{\mathbb{Q}}))\) the canonical class of the (compact connected) complex surface containing a global spherical shell. Assume S to be minimal and \(b_ 1(S)>0\). According to the classification of such surfaces due to Enoki and \textit{I. Nakamura} [Invent. Math. 78, 393-443 (1984; Zbl 0575.14033)] there remains only one class whose \(K_ S\) is to be calculated, the so-called CB-surface (by definition, containing only a finite number of curves, which are rational and whose configuration is a cycle with linear branches sprouting from the cycle). The canonical class can be expressed by using intersection matrices obtained by Nakamura (ibid.). - The article is just an announcement of the result.