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Fibered algebraic surfaces with low slope. (English) Zbl 0596.14028
One studies the properties of a complex surface of general type with a fibration \(f:\quad S\to C\) such that \(\omega^ 2_{S/C}<4\cdot \deg (f_*\omega_{S/C})\). For such a surface the image of the \(\pi_ 1\) of a fibre of f in \(\pi_ 1(S)\) is trivial, unless the fibres of f are hyperelliptic, and this image is \({\mathbb{Z}}_ 2\). One also shows a lower bound for \(\omega^ 2_{S/C}\), studies the stability of \(f_*\omega_{S/C}\), and gives several examples.

MSC:
14J25 Special surfaces
14E20 Coverings in algebraic geometry
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