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M.Ed. Maximilian Holdt

Researcher


Christian-Albrechts-Universität zu Kiel

E-mail: holdt(at)math.uni-kiel.de
Telephone: 0431/8803669
Homepage: https://www.math.uni-kiel.de/geometrie/d…

Project

77Asymptotic geometry of the Higgs bundle moduli space II

Publications within SPP2026

We use the theory of Gaiotto, Moore and Neitzke to construct a set of Darboux coordinates on the moduli space \(\mathcal{M}\) of weakly parabolic \(SL(2,\mathbb{C})\)-Higgs bundles. For generic Higgs bundles\((\mathcal{E},R\Phi)\) with \(R\gg 0\) the coordinates are shown to be dominated by a leading term that is given by the coordinates for a corresponding simpler space of limiting configurations and we prove that the deviation from the limiting term is given by a remainder that is exponentially suppressed in \(R\).

    

    We then use this result to solve an associated Riemann-Hilbert problem and construct a twistorial hyperkähler metric \(g_{\text{twist}}\) on \(\mathcal{M}\). Comparing this metric to the simpler semiflat metric \(g_{\text{sf}}\), we show that their difference is \(g_{\text{twist}}-g_{\text{sf}}=O\left(e^{-\mu R}\right)\), where \(\mu\) is a minimal period of the determinant of the Higgs field.

 

Related project(s):
77Asymptotic geometry of the Higgs bundle moduli space II

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