On complex surfaces with 5 or 6 semistable singular fibers over 1 (Q1771981)

Denote by \(X\) a complex smooth projective surface, and by \(f:X\rightarrow C\) a fibration over a curve \(C\) of genus \(g\geq 2\). The fibration \(f\) is called isotrivial if all smooth fibres are isomorphic to a fixed curve. A result of \textit{A. Beauville} [Astérisque 86, 97--108 (1981; Zbl 0502.14009)] states that a non-isotrivial fibration with \(C={\mathbb P}^1\) has at least three singular fibres. The present paper gives some information about the structure of \(X\) when \(C={\mathbb P}^1\) and there are \(5\) or \(6\) singular fibres.