Iterated fibre sums of algebraic Lefschetz fibrations

M. J. D. Hamilton

doi:10.1093/qmath/hat049

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arXiv · 1209.2653

Iterated fibre sums of algebraic Lefschetz fibrations

M. J. D. Hamilton

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Abstract

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz pencil on a simply-connected minimal surface of general type we partially calculate the Seiberg-Witten invariants of the fibre sum M(n) using a formula of Morgan-Szabo-Taubes. As an application we derive an obstruction for self-diffeomorphisms of the boundary of the tubular neighbourhood of a general fibre in M(n) to extend over the complement of the neighbourhood. Similar obstructions are known in the case of elliptic surfaces.

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BibTeX RIS

M. J. D. Hamilton. 2012-09-12. Iterated fibre sums of algebraic Lefschetz fibrations. https://doi.org/10.1093/qmath/hat049

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