Construction of automorphisms of hyperkähler manifolds
Let M be an irreducible holomorphic symplectic (hyperkähler) manifold. If b 2 (M ) > 5, we construct a deformation M 0 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 b 2 (M ) > 14, similarly, we construct a deformation which admits a parabolic automorphism (and many other automorphisms as well).