Integrable systems and Special K\"ahler metrics

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.