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

Let $X$ be a toric Del-Pezzo surface and let $Crit(W) \subset ($\mathbb{C}$^{\ast})^n$ be the solution scheme of the Landau-Ginzburg system of equations. Denote by $X^{\circ }$ the polar variety of $X$. Our aim in this work is to describe a map $L:Crit(W)\to Fu{k}_{trop}(X^{\circ })$ whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles.