Mathematical Research Letters

Volume 17 (2010)

Number 6

Exact Lefschetz fibrations associated with dimer models

Pages: 1029 – 1040



Masahiro Futaki (The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan)

Kazushi Ueda (Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan)


We associate an exact Lefschetz fibration with a pair of a consistent dimer model and an internal perfect matching on it, whose Fukaya category is derived-equivalent to the category of representations of the directed quiver with relations associated with the pair. As a corollary, we obtain a version of homological mirror symmetry for two-dimensional toric Fano stacks.

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