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arXiv · 2409.16625

Moduli Spaces of the Basic Hitchin Equation on Sasakian Threefolds

Takashi Ono
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Abstract

In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct the moduli space of the basic Hitchin equation and show that such a space admits a hyperK\"ahler metric. This also shows that the moduli space of flat bundles over Sasakian threefolds admits a hyperK\"ahler metric. We also calculate the dimension of the moduli space.

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Takashi Ono. 2024-09-25. Moduli Spaces of the Basic Hitchin Equation on Sasakian Threefolds. https://arxiv.org/abs/2409.16625

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