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

Abstract

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.

arXiv commentPublished in Journal of Mathematical Physics 2017 (Vol.58, Issue 3)

References in corpus (8)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
• Homogeneous coordinate rings and mirror symmetry for toric varieties
• Maximal lengths of exceptional collections of line bundles
• Derived categories for the working mathematician
• More about vanishing cycles and mutation
• On Landau-Ginzburg Systems and ${\mathcal{D}}^b(X)$ of projective bundles

Cited by in corpus (2)

• Gamma conjecture I for del Pezzo surfaces
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties