Construction of automorphisms of hyperkähler manifolds

Abstract

Let $M$ be an irreducible holomorphic symplectic (hyperkähler) manifold. If $b_2(M)\ge 5$, we construct a deformation $M^{\prime }$ 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 $b_2(M)\ge 14$, similarly, we construct a deformation which admits a parabolic automorphism.

16 pages, LaTeX

References in corpus (1)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum

Cited by in corpus (3)

• On the stable dynamical spectrum of complex surfaces
• Parabolic automorphisms of hyperkahler manifolds
• Special Hermitian structures on suspensions