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Construction of automorphisms of hyperkähler manifolds
- Part of
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- Journal:
- Compositio Mathematica / Volume 153 / Issue 8 / August 2017
- Published online by Cambridge University Press:
- 31 May 2017, pp. 1610-1621
- Print publication:
- August 2017
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- Article
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Let
$M$ be an irreducible holomorphic symplectic (hyperkähler) manifold. If 
$b_{2}(M)\geqslant 5$, 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 
$b_{2}(M)\geqslant 14$, similarly, we construct a deformation which admits a parabolic automorphism (and many other automorphisms as well).
