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arXiv · 1604.03079

Construction of automorphisms of hyperk\"ahler manifolds

Ekaterina Amerik·Misha Verbitsky
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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.

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Ekaterina Amerik, Misha Verbitsky. 2016-04-11. Construction of automorphisms of hyperk\"ahler manifolds. https://doi.org/10.1112/s0010437x17007138

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