Construction of automorphisms of hyperk\"ahler manifolds

Abstract

Let $M$ be an irreducible holomorphic symplectic (hyperk\"ahler) manifold. If $b_2(M)\geq 5$, 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 $b_2(M) \geq 14$, similarly, we construct a deformation which admits a parabolic automorphism.