 
Summary: Proceedings of 9th
GĻokova
GeometryTopology Conference,
pp, 1 10
Fiber sums of genus 2 Lefschetz fibrations
Denis Auroux
Abstract. Using the recent results of Siebert and Tian about the holomorphicity of
genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2
Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.
1. Introduction
Symplectic Lefschetz fibrations have been the focus of a lot of attention since the proof
by Donaldson that, after blowups, every compact symplectic manifold admits such struc
tures [3]. Genus 2 Lefschetz fibrations, where the first nontrivial topological phenomena
arise, have been particularly studied. Most importantly, it has recently been shown by
Siebert and Tian that every genus 2 Lefschetz fibration without reducible fibers and with
"transitive monodromy" is holomorphic [9]. The statement becomes false if reducible
singular fibers are allowed, as evidenced by the construction by Ozbagci and Stipsicz [7]
of genus 2 Lefschetz fibrations with noncomplex total space (similar examples have also
been constructed by Ivan Smith; the reader is also referred to the work of Amorīos et al [1]
and Korkmaz [5] for related constructions).
