On hyperelliptic $C^{\infty }$-Lefschetz fibrations of four-manifolds

Abstract

We show that hyperelliptic symplectic Lefschetz fibrations are symplectically birational to two-fold covers of rational ruled surfaces, branched in a symplectically embedded surface. This reduces the classification of genus 2 fibrations to the classification of certain symplectic submanifolds in rational ruled surfaces.

23 pages, 1 figure, Latex2e with AMS-fonts