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Generalizing work of Haydys and Hitchin, we prove the existence of ahyperholomorphic line bundle on certain hyperk\"ahler manifolds that do notnecessarily admit an $S^1$ action. As examples, we consider the moduli space of(non-strongly) parabolic Higgs bundles, the moduli space of solutions to Nahm'sequations, and Nakajima quiver varieties.

A hyperholomorphic line bundle on certain hyperk\"ahler manifolds not admitting an $S^1$-symmetry