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arXiv · 1810.01554

Exponential Decay for the Asymptotic Geometry of the Hitchin Metric

Laura Fredrickson
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Abstract

We consider Hitchin's hyperk\"ahler metric $g_{L^2}$ on the $SU(n)$-Hitchin moduli space moduli space over a compact Riemann surface. We prove that the difference between the metric $g_{L^2}$ and a simpler "semiflat" hyperk\"ahler metric $g_{\mathrm{sf}}$ is exponentially-decaying along generic rays in the Hitchin moduli space, as conjectured by Gaiotto-Moore-Neitzke.

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Laura Fredrickson. 2018-10-03. Exponential Decay for the Asymptotic Geometry of the Hitchin Metric. https://doi.org/10.1007/s00220-019-03547-9

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