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arXiv · 2503.23891

Monodromy of Darboux transformations of polarised curves

Joseph Cho·Katrin Leschke·Yuta Ogata
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Abstract

We show that every finite type polarised curve in the conformal $2$-sphere with a polynomial conserved quantity admits a resonance point, under a non-orthogonality assumption on the conserved quantity. Using this fact, we deduce that every finite type curve polarised by space form arc-length in the conformal $2$-sphere admits a resonance point, possibly on a multiple cover.

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Joseph Cho, Katrin Leschke, Yuta Ogata. 2025-03-31. Monodromy of Darboux transformations of polarised curves. https://arxiv.org/abs/2503.23891

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