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Topological Euler numbers in a semi-stable degeneration of surfaces. (English) Zbl 1052.14040

The author proves a lower bound for the topological Euler number of surfaces in a semistable degeneration by means of Euler numbers of components and double curves in the central fibre. As an application he proves that if we have a semistable degeneration with a minimal Enriques surface as a general fibre and such that the central fibre is normal then the number of singularities of the central fibre is at most \(10\). He also gives an example showing that this upper bound can be attained.

MSC:

14J28 \(K3\) surfaces and Enriques surfaces
14D06 Fibrations, degenerations in algebraic geometry
14F45 Topological properties in algebraic geometry
14J17 Singularities of surfaces or higher-dimensional varieties
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