Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
Symplectic Geometry
2015-05-13 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0907.2063,
title = {Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry},
author = {Paul Seidel},
journal= {arXiv preprint arXiv:0907.2063},
year = {2015}
}
Comments
v2: slightly expanded exposition