Hirota varieties and rational nodal curves

Article Computer Science, Theory & Methods

KP solitons from tropical limits

Daniele Agostini et al.

Summary: In this study, we investigate the solutions to the Kadomtsev-Petviashvili equation with tropical degenerations of underlying algebraic curves. We show that Riemann's theta function can be expressed as a finite exponential sum supported on a Delaunay polytope. We introduce the Hirota variety as a parameterization for all tau functions arising from such a sum. Furthermore, we compute tau functions from points on the Sato Grassmannian and propose an algorithm to find soliton solutions from rational nodal curves.

JOURNAL OF SYMBOLIC COMPUTATION (2023)

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Article Mathematics, Applied

The Dubrovin threefold of an algebraic curve

Daniele Agostini et al.

Summary: The study uses methods from nonlinear algebra to investigate parametrizations and defining ideals of Dubrovin threefolds, highlighting the contrast between transcendental representations and exact algebraic computations. The main result is a toric degeneration of the Dubrovin threefold into the product of the underlying canonical curve and a weighted projective plane.

NONLINEARITY (2021)

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Article Mathematics

An explicit solution to the weak Schottky problem

Hershel M. Farkas et al.

Summary: In the spirit of Riemann and Schottky, researchers provide an explicit weak solution to the Schottky problem for any genus g. By applying a specific Schottky-Jung proportionality, a collection of polynomials in genus g theta constants is constructed to include the locus of Jacobians of genus g curves as an irreducible component.

ALGEBRAIC GEOMETRY (2021)

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Article Physics, Mathematical