Bipartite graphs and mirror coamoebae

Harold Williams
University of Southern California (USC)

We discuss joint work with Chris Kuo and earlier work with David Treumann and Eric Zaslow on which it builds. This earlier work gave a combinatorial description of how homological mirror symmetry acts on one-dimensional coherent sheaves on a toric surface. Namely, it takes them to Lagrangians which are perturbations of the conormals to a suitable bipartite graph in $T^2$. The map on moduli is implemented by the Kasteleyn operator of the graph, hence is governed by the enumeration of perfect matchings. In current work we show that such a description holds more generally for coherent sheaves of codimension one on a toric variety of dimension $n \geq 2$, now involving bipartite graphs in $T^n$.

Presentation (PDF File)

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