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 H 2(X, ℤ) is isomorphic to E 8(−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.
|Titolo:||Symplectic involutions on deformations of K3|
MONGARDI, GIOVANNI (Primo)
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||ago-2012|
|Digital Object Identifier (DOI):||10.2478/s11533-012-0073-z|
|Appare nelle tipologie:||01 - Articolo su periodico|