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Real algebraic surfaces with rational or elliptic fiberings. (English) Zbl 0558.14022

The main parts of the paper are devoted to the study of ruled and elliptic real algebraic surfaces. The topological structure of the real part X(\({\mathbb{R}})\) of a ruled surface X over \({\mathbb{R}}\) is completely determined. In the more complicated case of a (B-minimal) elliptic fibering \(\pi: X\to B\) the singular fibers are studied. In this part, the fibers in a neighbourhood of a special point \(b_ 0\) of B(\({\mathbb{R}})\) (i.e. the fiber in \(b_ 0\) is singular), the group structure of \(Reg(\pi^{-1}(b_ 0))({\mathbb{R}})\), and the algebraic structure of \(\pi^{-1}(b_ 0)\) are determined. Finally examples for some of the situations derived in this way, are constructed as well as a \(K_ 3\) surface X, such that X(\({\mathbb{R}})\) is connected, non-orientable and of Euler characteristic -18.
Reviewer: H.W.Schülting

MSC:

14Pxx Real algebraic and real-analytic geometry
14J10 Families, moduli, classification: algebraic theory
14J25 Special surfaces
14F45 Topological properties in algebraic geometry
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
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References:

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