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Zbl 0634.14023
Nishiguchi, Kenji
Canonical bundles of compact complex surfaces containing global spherical shells.
(English)
[J] Proc. Japan Acad., Ser. A 62, 234-237 (1986). ISSN 0386-2194

The author determines numerically (i.e. in $H\sp 2(S,{\bbfQ}))$ the canonical class of the (compact connected) complex surface containing a global spherical shell. Assume S to be minimal and $b\sb 1(S)>0$. According to the classification of such surfaces due to Enoki and {\it I. Nakamura} [Invent. Math. 78, 393-443 (1984; Zbl 0575.14033)] there remains only one class whose $K\sb S$ 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.
[Y.Namikawa]
MSC 2000:
*14J25 Special surfaces
32J15 Compact surfaces (analytic spaces)
14C30 Transcendental methods

Keywords: canonical class; global spherical shell; CB-surface; intersection matrices

Citations: Zbl 0575.14033

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