arXiv subjects
Publications and source records attributed to Giovanni Mongardi.
In the present paper we prove that finite symplectic groups of automorphisms of manifolds of k3^[n] type can be obtained by deforming natural morphisms arising from K3 surfaces if and only if they satisfy a certain numerical condition.
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.
The present paper proves that finite symplectic groups of automorphisms of hyperkähler fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $Co_1$. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.
Let X be a Hyperkähler variety deformation equivalent to the Hilbert square on a K3 surface and let f be an involution preserving the symplectic form. We prove that the fixed locus of f consists of 28 isolated points and 1 K3 surface, moreover the anti-invariant lattice of the induced involution on H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting of one such variety and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a Nikulin involution on the K3 surface.