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arXiv · 1303.4670

Automorphisms of hyperk\"ahler manifolds

Giovanni Mongardi
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Abstract

The present paper provides several results on automorphisms of hyperk\"ahler (or irreducible holomorphic symplectic) manifolds. In particular it focuses on the symplectic case and contains a classification of prime order symplectic automorphisms on deformations of the Hilbert scheme of two points on a K3 surface and, with additional hypothesis, also on Hilbert schemes of n points on a K3 surface. We also give numerical conditions to establish whether a symplectic automorfism of order 2,3 and 5 on a deformation of the Hilbert scheme of two points on a K3 surface is standard. Moreover we also give various examples.

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Giovanni Mongardi. 2013-03-19. Automorphisms of hyperk\"ahler manifolds. https://arxiv.org/abs/1303.4670

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