Dubroving threefold of an algebraic curve

Dr. Türkü Özlüm Çelik

08 October 2021 17:00

Abstract

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 equations of Dubrovin threefolds. We highlight the dichotomy between transcendental representations and exact algebraic computations. Finally, a natural question arises: what happens to the Dubrovin threefold when the underlying curve degenerates?