Integrable systems and Special K\"ahler metrics

Nigel Hitchin

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arXiv · 1910.05170

Integrable systems and Special K\"ahler metrics

Nigel Hitchin

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Abstract

We describe the Special K\"ahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the K\"ahler potential. This extends to the case of a singular spectral curve and we show that this defines the Special K\"ahler structure on certain natural integrable subsystems. Examples include the extreme case where the metric is flat.

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Nigel Hitchin. 2019-10-11. Integrable systems and Special K\"ahler metrics. https://arxiv.org/abs/1910.05170

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