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Being inspired by a work of Curtis T. McMullen about a very impressive automorphism of a K3 surface of Picard number zero, we shall clarify the structure of the bimeromorphic automorphism group of a non-projective hyperk\"ahler manifold, up to finite group factor. We also discuss relevant topics, especially, new counterexamples of Kodaira's problem about algebraic approximation of a compact K\"ahler manifold.

Bimeromorphic automorphism groups of non-projective hyperkähler manifolds—a note inspired by C.T. McMullen