Dimer models and exceptional collections

TL;DR

This paper constructs a full strong exceptional collection of line bundles on two-dimensional smooth toric weak Fano stacks, linking algebraic geometry with dimer models and quiver representations.

Contribution

It introduces a novel method to realize exceptional collections via dimer models, connecting toric geometry with combinatorial quiver theory.

Findings

Constructs full strong exceptional collections on toric weak Fano stacks.

Shows the endomorphism algebra corresponds to a dimer model's quiver.

Establishes a link between algebraic geometry and dimer model combinatorics.

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.