Hirota varieties

We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. We study the Hirota variety associated to familiar Delaunay polytopes, in particular characterizing it for the g-cube.

If time permits, we will also compute tau functions from points on the Sato Grassmannian that represent Riemann-Roch spaces and present an algorithm that finds a soliton solution from a rational nodal curve.