# 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.

## Key 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.

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Source: https://tomesphere.com/paper/0911.4529