On exceptional collections of line bundles and mirror symmetry for toric Del-Pezzo surfaces

摘要

Let X be a toric Del-Pezzo surface and let Crit(W) subset of (C*) (n) be the solution scheme of the Landau-Ginzburg system of equations. Denote by X degrees the polar variety of X. Our aim in this work is to describe a map L : Crit(W) -> Fuk(trop)(X degrees) whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles. Published by AIP Publishing.