The Dubrovin threefold of an algebraic curve

The solutions to the Kadomtsev–Petviashvili equation that arise from a fixed complex algebraic curve are parametrized by a threefold in a weighted projective space, which we name after Boris Dubrovin. Current methods from nonlinear algebra are applied to study parametrizations and defining ideals of...

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Bibliographic Details
Published in:Nonlinearity 2021-06, Vol.34 (6), p.3783-3812
Main Authors: Agostini, Daniele, Çelik, Türkü Özlüm, Sturmfels, Bernd
Format: Article
Language:English
Subjects:
KP equation
Riemann surfaces
Schottky problem
theta function
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Summary:The solutions to the Kadomtsev–Petviashvili equation that arise from a fixed complex algebraic curve are parametrized by a threefold in a weighted projective space, which we name after Boris Dubrovin. Current methods from nonlinear algebra are applied to study parametrizations and defining ideals of Dubrovin threefolds. We highlight the dichotomy between transcendental representations and exact algebraic computations. Our main result on the algebraic side is a toric degeneration of the Dubrovin threefold into the product of the underlying canonical curve and a weighted projective plane.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/abf08c