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For questions about or involving fibrations which are maps which satisfy the homotopy lifting property for all spaces.
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Isotrivial fibrations over $\mathbb P^1$
The singularities of $A \times B/G $ are cyclic quotient singularities, and solving them one gets a smooth surface with an isotrivial fibration birational to the starting fibration such that all singular … If the genus of the fibre is zero every book on algebraic surface tells you that the fibration is birational to a bundle, and then the same argument applies. …