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Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions
Published online by Cambridge University Press: 24 August 2023
Abstract
We classify fibrations of abstract $3$-regular GKM graphs over $2$-regular ones, and show that all fibrations satisfying the known necessary conditions for realizability are, in fact, realized as the projectivization of equivariant complex rank-$2$ vector bundles over quasitoric $4$-manifolds or $S^4$. We investigate the existence of invariant (stable) almost complex, symplectic, and Kähler structures on the total space. In this way, we obtain infinitely many Kähler manifolds with Hamiltonian non-Kähler actions in dimension $6$ with prescribed one-skeleton, in particular with a prescribed number of isolated fixed points.
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- © 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence