Hirota Varieties and Rational Nodal Curves

TL;DR

This paper investigates the Hirota variety associated with rational nodal curves, identifying its main component and solving a weak Schottky problem up to genus nine using computational methods.

Contribution

It characterizes the main component of the Hirota variety for rational nodal curves and solves the weak Schottky problem up to genus nine computationally.

Findings

Identification of the main component as an irreducible subvariety.

Solution of the weak Schottky problem for rational nodal curves up to genus nine.

Use of computational tools to analyze the Hirota variety.

Abstract

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.