Abstract

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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