Giovanni Mongardi

Symplectic involutions on deformations of K3[2]

Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H2(X, ℤ) is isomorphic to E8(−2). Finally we show that any couple consisting of one such manifold 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 symplectic involution on the K3 surface.

On natural deformations of symplectic automorphisms of manifolds of type

Abstract In the present paper, we prove that finite symplectic groups of automorphisms of manifolds of K 3 [ n ] type can be obtained by deforming natural morphisms arising from K3 surfaces if and only if they satisfy a certain numerical condition.

Induced automorphisms on irreducible symplectic manifolds

We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of K3-type is, in fact, induced by an automorphism of a K3 surface and the manifold is a moduli space of stable objects on the K3. This criterion is applied to the classification of non-symplectic prime order automorphisms on manifolds of K3-type and we prove that almost all cases are covered. Variations of this notion and the above criterion are introduced and discussed for the other known deformation types of irreducible symplectic manifolds. Furthermore we provide a description of the Picard lattice of several irreducible symplectic manifolds having a lagrangian fibration.

Towards a classification of symplectic automorphisms on manifolds of \(K3^{[n]}\) type

The present paper is devoted to the classification of symplectic automorphisms of some hyperkählermanifolds. The result presented here is a proof that all finite groups of symplectic automorphisms of manifolds of

A note on the K\"ahler and Mori cones of hyperk\"ahler manifolds

K3^{[n]}

Isometries of Ideal Lattices and Hyperkähler Manifolds

K3[n] typeare contained in Conway’s group

Severi varieties and Brill-Noether theory of curves on abelian surfaces

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