A hyperholomorphic line bundle on certain hyperkähler manifolds not admitting an $S^1$-symmetry

Abstract

Generalizing work of Haydys and Hitchin, we prove the existence of a hyperholomorphic line bundle on certain hyperkähler manifolds that do not necessarily 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's equations, and Nakajima quiver varieties.

31 pages. Comments welcomed. New in v2 are sections 5.1.1 and 5.2

References in corpus (2)

• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• On a hyperholomorphic line bundle over the Coulomb branch