Dimer models and exceptional collections

Abstract

We construct a full strong exceptional collection consisting of line bundles on any two-dimensional smooth toric weak Fano stack. The total endomorphism algebra of the resulting collection is isomorphic to the path algebra of a quiver with relations associated with a dimer model and a perfect matching on it.

18 pages, no figures. v2: added Remark 7.4 and Section 8

References in corpus (7)

• Dimer models and toric diagrams
• Maximal lengths of exceptional collections of line bundles
• On moduli spaces of quiver representations associated with dimer models
• Crepant resolutions and brane tilings I: Toric realization
• A note on consistency conditions on dimer models
• Crepant resolutions and brane tilings II: Tilting bundles
• Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions

Cited by in corpus (11)

• Maximal lengths of exceptional collections of line bundles
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Dual torus fibrations and homological mirror symmetry for A_n-singularities
• Remarks on quiver gauge theories from open topological string theory
• The derived contraction algebra
• Exceptional collections on toric Fano threefolds and birational geometry
• Exact Lefschetz fibrations associated with dimer models
• Noncommutative mirror symmetry for punctured surfaces
• On $\mathrm{H}-$trivial line bundles on toric DM stacks of dimension two
• Equivariant derived category of flat families
• On $\mathrm{H}-$trivial line bundles on toric DM stacks of dim $\ge 3$