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arXiv · 2102.10853

Geometry of the Space of Sections of Twistor Spaces with Circle Action

Florian Beck·Indranil Biswas·Sebastian Heller·Markus Röser
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Abstract

We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space carries a line bundle with meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah-Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and furthermore the critical points of this moment map are studied. Particular emphasis is given to the example of Deligne-Hitchin moduli spaces.

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Florian Beck, Indranil Biswas, Sebastian Heller, Markus Röser. 2021-02-22. Geometry of the Space of Sections of Twistor Spaces with Circle Action. https://doi.org/10.3842/sigma.2026.008

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