The inverse spectral map for dimers
Algebraic Geometry
2023-08-25 v2 Combinatorics
Abstract
In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer cluster integrable system its spectral data, is birational by constructing an inverse map using theta functions on Jacobians of spectral curves. We provide an alternate construction of the inverse map that involves only rational functions in the spectral data.
Cite
@article{arxiv.2207.10146,
title = {The inverse spectral map for dimers},
author = {Terrence George and Alexander Goncharov and Richard Kenyon},
journal= {arXiv preprint arXiv:2207.10146},
year = {2023}
}
Comments
46 pages, 13 figures, final version to appear in Mathematical Physics, Analysis and Geometry