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arXiv · 1408.4844

Singularities of integrable systems and nodal curves

Anton Izosimov
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Abstract

The relation between integrable systems and algebraic geometry is known since the XIXth century. The modern approach is to represent an integrable system as a Lax equation with spectral parameter. In this approach, the integrals of the system turn out to be the coefficients of the characteristic polynomial $\chi$ of the Lax matrix, and the solutions are expressed in terms of theta functions related to the curve $\chi = 0$. The aim of the present paper is to show that the possibility to write an integrable system in the Lax form, as well as the algebro-geometric technique related to this possibility, may also be applied to study qualitative features of the system, in particular its singularities.

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Anton Izosimov. 2014-08-21. Singularities of integrable systems and nodal curves. https://arxiv.org/abs/1408.4844

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