Hyperelliptic Lefschetz fibrations and branched covering spaces

Terry Fuller

Vol. 196 (2000), No. 2, 369–393

DOI: 10.2140/pjm.2000.196.369

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.

Milestones

Received: 1 February 1999

Published: 1 December 2000