Kenta Hayano (Keio)
title:New counterexamples to Stipsicz's conjecture on
fiber-sum indecomposable Lefschetz fibrations
abstract: Stipsicz (and independently Smith) showed that a (4-dimensional) Lefschetz
fibration over the 2-sphere is fiber-sum indecomposable if it has a section with
self-intersection -1. Stipsicz's conjecture is the converse of this statement,
which is known to be false: there exist counterexamples with genus 2 (due to Y. Sato)
and genus 3 (due to Baykur-Hayano). In this talk, we will explain how to construct
counterexamples to Stipsicz's conjecture with any higher genera.
If time permits, we will also discuss (symplectic) Kodaira dimensions of these examples.
The results in this talk are based on joint work with Refik Inanc Baykur
(University of Massachusetts) and Naoyuki Monden (Okayama University).