Symplectic involutions on deformations of K3[2]

By Giovanni Mongardi. 2011

47 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/559956dfc7ec03f520a4bf6fe0cf3eb5afb7cf55

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. C. Camere
2. Samuel Boissière
3. A. Sarti
4. Marc A. Nieper-Wisskirchen
5. Giovanni Mongardi
6. Giancarlo Urzúa

In Mathematical Physics

1. C. Camere
2. Samuel Boissière
3. Marc A. Nieper-Wisskirchen
4. A. Sarti
5. Giovanni Mongardi

Citations in the corpus

• Smith theory and irreducible holomorphic symplectic manifolds (2012, background): “The following lemma is a direct generalization of Nikulin’s results [35], very close to those stated in Mongardi [32].”
• Classification of automorphisms on a deformation family of hyper-Kähler four-folds by $p$-elementary lattices (2014, background): “The interest in automorphisms of IHS manifold has grown up extremely in the last years (see [5, 12, 26, 33, 8, 9]) especially the study of automorphisms of prime order on IHS fourfolds deformation equivalent to the Hilbert scheme of two points on a K3 surface, that we call for short IHS−K3([2]).”