Dimer models and exceptional collections

2009/11/24 by Akira Ishii, Ishii, Akira, Kazushi Ueda +1
Mathematics · #14D21 #16G20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0911.4529

openalex publication_date 2009/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• Dimer models and toric diagrams
• A note on consistency conditions on dimer models
• Crepant resolutions and brane tilings II: Tilting bundles
• McKay equivalence for symplectic resolutions of singularities
• On moduli spaces of quiver representations associated with dimer models

Related

• Exact Lefschetz fibrations associated with dimer models
• Exceptional Collections of Line Bundles for Smooth Toric Fano Surfaces and Threefolds
• Dimer models and toric diagrams
• Exceptional Collections for Toric Fano Fourfolds
• DG quivers of smooth rational surfaces