A note on consistency conditions on dimer models
arXiv:1012.5449
Abstract
We show that for a non-degenerate dimer model, both the first consistency condition of Mozgovoy and Reineke and the properly-orderedness condition of Gulotta are equivalent to a condition on zigzag paths, which goes back to Hanany and Vegh. The last condition is used in arXiv:0905.0059 to study the behavior of a dimer model under the operation of removing a vertex from the lattice polygon and taking the convex hull of the rest.
17 pages, 23 figures; an expanded version of Section 5 of arXiv:0905.0059, to appear in RIMS Kokyuroku Bessatsu
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- A Dimer ABC
- A Comprehensive Survey of Brane Tilings
- Dimer models and exceptional collections
- Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
- Noetherian criteria for dimer algebras
- Combinatorial Reid's recipe for consistent dimer models
- Deformations of Dimer Models
- Perfect matching modules, dimer partition functions and cluster characters
- Geometric Reid's recipe for dimer models
- Strebel Differentials and stable Matrix Factorizations