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Twistor quotients of hyperkaehler manifolds

Roger Bielawski
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Abstract

We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding complex symplectic structure. Many (known and new) hyperkaehler manifolds arise as quotients in this setting. For example, all hyperkaehler structures on semisimple coadjoint orbits of a complex semisimple Lie group $G$ arise as such quotients of $T^*G$. The generalized Legendre transform construction of Lindstroem and Rocek is also explained in this framework.

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Roger Bielawski. 2000-06-20. Twistor quotients of hyperkaehler manifolds. https://arxiv.org/abs/math/0006142

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