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Hyperelliptic Lefschetz Fibrations And Branched Covering Spaces

Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over S2. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of an S2-bundle over S2, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes σ separating curves, we show that M is the relative minimalization of a Lefschetz fibration constructed as a 2-fold branched cover of ℂP2#(2σ + 1)ℂP2, branched over an embedded surface.

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