Symplectic involutions on deformations of K3^[2]
Algebraic Geometry
2012-05-23 v3
Abstract
Let X be a Hyperk\"{a}hler 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.
Keywords
Cite
@article{arxiv.1107.2854,
title = {Symplectic involutions on deformations of K3^[2]},
author = {Giovanni Mongardi},
journal= {arXiv preprint arXiv:1107.2854},
year = {2012}
}
Comments
Final version, to appear on Central European Journal of Mathematics