Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry

Details Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry

2009-07-12

arxiv.org/abs/0907.2063v2

Mathematics

Symplectic Geometry

v2: slightly expanded exposition

Scientific paper

We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.

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