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Proceedings of 9th Geometry-Topology Conference,

Summary: Proceedings of 9th
Geometry-Topology 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 blow-ups, every compact symplectic manifold admits such struc-
tures [3]. Genus 2 Lefschetz fibrations, where the first non-trivial 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 non-complex 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).


Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)


Collections: Mathematics