Producing a Poisson cluster variety using dimer models

In the coming two talks we will discuss a construction of a cluster variety with a Poisson structure, coming from bipartite graphs on the torus. This week will start with some definitions and motivation for Poisson varieties, and proceed to a construction of a cluster variety from a (Newton) polygon in the plane. We will see that every bipartite graph has a natural algebraic torus attached - the moduli space of line bundles on the graph. These tori glue together along mutations of the graph, giving a cluster variety.

Date published: Wednesday, November 9, 2022