Hyperelliptic Lefschetz fibrations and branched covering spaces

Details Hyperelliptic Lefschetz fibrations and branched covering spaces Hyperelliptic Lefschetz fibrations and branched covering spaces

1998-11-15

arxiv.org/abs/math/9811093v2

Mathematics

Geometric Topology

22 pages, 18 figures; main theorems changed from earlier version

Scientific paper

Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over the 2-sphere. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of a 2-sphere bundle over the 2-sphere, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes separating curves, we show that M is the relative minimalization of a Lefshetz fibration N, with N a 2-fold branched cover of a rational surface, branched over an embedded surface.

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