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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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References:
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