Hirota varieties and rational nodal curves

The Hirota variety parameterizes solutions to the KP equation arising from a degenerate Riemann theta function. In this work, we study in detail the Hirota variety arising from a rational nodal curve. Of particular interest is the irreducible subvariety defined as the image of a parameterization map, we call this the main component. Proving that this is an irreducible component of the Hirota variety corresponds to solving a weak Schottky problem for rational nodal curves. We solve this problem up to genus nine using computational tools.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this work, the Hirota variety arising from a rational nodal curve is studied, with a specific focus on its irreducible subvariety called the main component. Proving this to be an irreducible component corresponds to solving a weak Schottky problem for rational nodal curves. Computational tools are used to solve this problem up to genus nine.