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Working paper

Construction of automorphisms of hyperkahler manifolds

Let M be an irreducible holomorphic symplectic (hyperk¨ahler) manifold. If b2(M) >= 5, we construct a deformation M′ of M which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its action on the space of real (1, 1)-classes is hyperbolic. If b2(M) >= 14, similarly, we construct a deformation which admits a parabolic automorphism.