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We give explicit positive factorizations for a genus-19 Lefschetz fibration over the torus and a family of genus-4 Lefschetz fibrations over a genus-2 surface. All these examples have only three nodes, and their total spaces are symplectic 4-manifolds of general type on the Bogomolov-Miyaoka-Yau line. In the course of...
We show that not every symplectic Lefschetz fibration over the $2$--sphere admits a smooth section, settling a long-standing open problem. To prove this, we develop a method for studying sections via lifts of monodromy factorizations with point-pushing maps and the induced handle decomposition of the total space, and a...
We study relatively minimal Lefschetz fibrations over closed oriented surfaces whose monodromy extends over a fixed 3--dimensional handlebody. If $X$ is the total space and $\ell$ is the number of critical points, we prove that $\sigma(X)=-\ell$. Such fibrations with $\ell>0$ exist precisely for fiber genus $g\geq3$ an...
We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental...
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