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arxiv: 0911.4529 · v2 · pith:2KNJC2UInew · submitted 2009-11-24 · 🧮 math.AG

Dimer models and exceptional collections

Akira Ishii , Kazushi Ueda This is my paper
classification 🧮 math.AG
keywords algebracollectiondimerexceptionalassociatedbundlescollectionsconsisting
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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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  1. Higher hereditary algebras and toric Fano stacks of Picard number one or two

    math.AG 2025-11 unverdicted novelty 7.0

    Classifies d-tilting line bundles on toric Fano stacks of Picard number 1 or 2 via upper sets in posets and establishes correspondences to d-representation infinite algebras of types à and Ãà with closure under d-APR tilts.