Automorphisms of hyperkähler manifolds
Abstract
The present paper provides several results on automorphisms of hyperkähler (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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2013
- DOI:
- 10.48550/arXiv.1303.4670
- arXiv:
- arXiv:1303.4670
- Bibcode:
- 2013arXiv1303.4670M
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14J50
- E-Print:
- This is my PhD Thesis with the University of RomaTRE. Contains arXiv 1112:5073 and 1107:2854