Fibered algebraic surfaces with low slope (Q1078272)

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.