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We prove that the image of the pluricanonical representation of a group ofbimeromorphic automorphisms of a complex manifold has bounded finite subgroups.As a consequence, we show that the group of bimeromorphic automorphisms of an$n$-dimensional complex manifold whose Kodaira dimension is at least $n-2$,satisfies the Jordan property.

Jordan property for groups of bimeromorphic self-maps of complex manifolds with large Kodaira dimension