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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0073-z,
author = {Giovanni Mongardi},
title = {Symplectic involutions on deformations of K3[2]},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1472-1485},
zbl = {1284.14052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0073-z}
}
Giovanni Mongardi. Symplectic involutions on deformations of K3[2]. Open Mathematics, Tome 10 (2012) pp. 1472-1485. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0073-z/
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